Rajesh Ranganath

Lily H. Zhang, Veronica Tozzo, John M. Higgins et al.

Permutation invariant neural networks are a promising tool for making predictions from sets. However, we show that existing permutation invariant architectures, Deep Sets and Set Transformer, can suffer from vanishing or exploding gradients when they are deep. Additionally, layer norm, the normalization of choice in Set Transformer, can hurt performance by removing information useful for prediction. To address these issues, we introduce the clean path principle for equivariant residual connections and develop set norm, a normalization tailored for sets. With these, we build Deep Sets++ and Set Transformer++, models that reach high depths with comparable or better performance than their original counterparts on a diverse suite of tasks. We additionally introduce Flow-RBC, a new single-cell dataset and real-world application of permutation invariant prediction. We open-source our data and code here: https://github.com/rajesh-lab/deep_permutation_invariant.

Rhys Compton, Lily Zhang, Aahlad Puli et al.

In machine learning, incorporating more data is often seen as a reliable strategy for improving model performance; this work challenges that notion by demonstrating that the addition of external datasets in many cases can hurt the resulting model's performance. In a large-scale empirical study across combinations of four different open-source chest x-ray datasets and 9 different labels, we demonstrate that in 43% of settings, a model trained on data from two hospitals has poorer worst group accuracy over both hospitals than a model trained on just a single hospital's data. This surprising result occurs even though the added hospital makes the training distribution more similar to the test distribution. We explain that this phenomenon arises from the spurious correlation that emerges between the disease and hospital, due to hospital-specific image artifacts. We highlight the trade-off one encounters when training on multiple datasets, between the obvious benefit of additional data and insidious cost of the introduced spurious correlation. In some cases, balancing the dataset can remove the spurious correlation and improve performance, but it is not always an effective strategy. We contextualize our results within the literature on spurious correlations to help explain these outcomes. Our experiments underscore the importance of exercising caution when selecting training data for machine learning models, especially in settings where there is a risk of spurious correlations such as with medical imaging. The risks outlined highlight the need for careful data selection and model evaluation in future research and practice.

Shi-ang Qi, Neeraj Kumar, Mahtab Farrokh et al.

One straightforward metric to evaluate a survival prediction model is based on the Mean Absolute Error (MAE) -- the average of the absolute difference between the time predicted by the model and the true event time, over all subjects. Unfortunately, this is challenging because, in practice, the test set includes (right) censored individuals, meaning we do not know when a censored individual actually experienced the event. In this paper, we explore various metrics to estimate MAE for survival datasets that include (many) censored individuals. Moreover, we introduce a novel and effective approach for generating realistic semi-synthetic survival datasets to facilitate the evaluation of metrics. Our findings, based on the analysis of the semi-synthetic datasets, reveal that our proposed metric (MAE using pseudo-observations) is able to rank models accurately based on their performance, and often closely matches the true MAE -- in particular, is better than several alternative methods.

Wouter A. C. van Amsterdam, Pim A. de Jong, Joost J. C. Verhoeff et al.

In cancer research there is much interest in building and validating outcome predicting outcomes to support treatment decisions. However, because most outcome prediction models are developed and validated without regard to the causal aspects of treatment decision making, many published outcome prediction models may cause harm when used for decision making, despite being found accurate in validation studies. Guidelines on prediction model validation and the checklist for risk model endorsement by the American Joint Committee on Cancer do not protect against prediction models that are accurate during development and validation but harmful when used for decision making. We explain why this is the case and how to build and validate models that are useful for decision making.

Yuxuan Hu, Albert Lui, Mark Goldstein et al.

Myocardial infarction and heart failure are major cardiovascular diseases that affect millions of people in the US. The morbidity and mortality are highest among patients who develop cardiogenic shock. Early recognition of cardiogenic shock is critical. Prompt implementation of treatment measures can prevent the deleterious spiral of ischemia, low blood pressure, and reduced cardiac output due to cardiogenic shock. However, early identification of cardiogenic shock has been challenging due to human providers' inability to process the enormous amount of data in the cardiac intensive care unit (ICU) and lack of an effective risk stratification tool. We developed a deep learning-based risk stratification tool, called CShock, for patients admitted into the cardiac ICU with acute decompensated heart failure and/or myocardial infarction to predict onset of cardiogenic shock. To develop and validate CShock, we annotated cardiac ICU datasets with physician adjudicated outcomes. CShock achieved an area under the receiver operator characteristic curve (AUROC) of 0.820, which substantially outperformed CardShock (AUROC 0.519), a well-established risk score for cardiogenic shock prognosis. CShock was externally validated in an independent patient cohort and achieved an AUROC of 0.800, demonstrating its generalizability in other cardiac ICUs.

Aahlad Puli, Lily Zhang, Yoav Wald et al.

Common explanations for shortcut learning assume that the shortcut improves prediction under the training distribution but not in the test distribution. Thus, models trained via the typical gradient-based optimization of cross-entropy, which we call default-ERM, utilize the shortcut. However, even when the stable feature determines the label in the training distribution and the shortcut does not provide any additional information, like in perception tasks, default-ERM still exhibits shortcut learning. Why are such solutions preferred when the loss for default-ERM can be driven to zero using the stable feature alone? By studying a linear perception task, we show that default-ERM's preference for maximizing the margin leads to models that depend more on the shortcut than the stable feature, even without overparameterization. This insight suggests that default-ERM's implicit inductive bias towards max-margin is unsuitable for perception tasks. Instead, we develop an inductive bias toward uniform margins and show that this bias guarantees dependence only on the perfect stable feature in the linear perception task. We develop loss functions that encourage uniform-margin solutions, called margin control (MARG-CTRL). MARG-CTRL mitigates shortcut learning on a variety of vision and language tasks, showing that better inductive biases can remove the need for expensive two-stage shortcut-mitigating methods in perception tasks.

Raghav Singhal, Mark Goldstein, Rajesh Ranganath

Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality. For example, extending the inference process with auxiliary variables leads to improved sample quality. While there are many such multivariate diffusions to explore, each new one requires significant model-specific analysis, hindering rapid prototyping and evaluation. In this work, we study Multivariate Diffusion Models (MDMs). For any number of auxiliary variables, we provide a recipe for maximizing a lower-bound on the MDMs likelihood without requiring any model-specific analysis. We then demonstrate how to parameterize the diffusion for a specified target noise distribution; these two points together enable optimizing the inference diffusion process. Optimizing the diffusion expands easy experimentation from just a few well-known processes to an automatic search over all linear diffusions. To demonstrate these ideas, we introduce two new specific diffusions as well as learn a diffusion process on the MNIST, CIFAR10, and ImageNet32 datasets. We show learned MDMs match or surpass bits-per-dims (BPDs) relative to fixed choices of diffusions for a given dataset and model architecture.

Raghav Singhal, Mukund Sudarshan, Anish Mahishi et al.

Early detection of many life-threatening diseases (e.g., prostate and breast cancer) within at-risk population can improve clinical outcomes and reduce cost of care. While numerous disease-specific "screening" tests that are closer to Point-of-Care (POC) are in use for this task, their low specificity results in unnecessary biopsies, leading to avoidable patient trauma and wasteful healthcare spending. On the other hand, despite the high accuracy of Magnetic Resonance (MR) imaging in disease diagnosis, it is not used as a POC disease identification tool because of poor accessibility. The root cause of poor accessibility of MR stems from the requirement to reconstruct high-fidelity images, as it necessitates a lengthy and complex process of acquiring large quantities of high-quality k-space measurements. In this study we explore the feasibility of an ML-augmented MR pipeline that directly infers the disease sidestepping the image reconstruction process. We hypothesise that the disease classification task can be solved using a very small tailored subset of k-space data, compared to image reconstruction. Towards that end, we propose a method that performs two tasks: 1) identifies a subset of the k-space that maximizes disease identification accuracy, and 2) infers the disease directly using the identified k-space subset, bypassing the image reconstruction step. We validate our hypothesis by measuring the performance of the proposed system across multiple diseases and anatomies. We show that comparable performance to image-based classifiers, trained on images reconstructed with full k-space data, can be achieved using small quantities of data: 8% of the data for detecting multiple abnormalities in prostate and brain scans, and 5% of the data for knee abnormalities. To better understand the proposed approach and instigate future research, we provide an extensive analysis and release code.

Aahlad Puli, Nitish Joshi, Yoav Wald et al.

In prediction tasks, there exist features that are related to the label in the same way across different settings for that task; these are semantic features or semantics. Features with varying relationships to the label are nuisances. For example, in detecting cows from natural images, the shape of the head is semantic but because images of cows often have grass backgrounds but not always, the background is a nuisance. Models that exploit nuisance-label relationships face performance degradation when these relationships change. Building models robust to such changes requires additional knowledge beyond samples of the features and labels. For example, existing work uses annotations of nuisances or assumes ERM-trained models depend on nuisances. Approaches to integrate new kinds of additional knowledge enlarge the settings where robust models can be built. We develop an approach to use knowledge about the semantics by corrupting them in data, and then using the corrupted data to produce models which identify correlations between nuisances and the label. Once these correlations are identified, they can be used to adjust for where nuisances drive predictions. We study semantic corruptions in powering different spurious-correlation avoiding methods on multiple out-of-distribution (OOD) tasks like classifying waterbirds, natural language inference (NLI), and detecting cardiomegaly in chest X-rays.

Rico Angell, Raghav Singhal, Zachary Horvitz et al.

Language models are increasingly capable and are being rapidly deployed on a population-level scale. As a result, the safety of these models is increasingly high-stakes. Fortunately, advances in alignment have significantly reduced the likelihood of harmful model outputs. However, when models are queried billions of times in a day, even rare worst-case behaviors will occur. Current safety evaluations focus on capturing the distribution of inputs that yield harmful outputs. These evaluations disregard the probabilistic nature of models and their tail output behavior. To measure this tail risk, we propose a method to efficiently estimate the probability of harmful outputs for any input query. Instead of naive brute-force sampling from the target model, where harmful outputs could be rare, we operationalize importance sampling by creating unsafe versions of the target model. These unsafe versions enable sample-efficient estimation by making harmful outputs more probable. On benchmarks measuring misuse and misalignment, these estimates match brute-force Monte Carlo estimates using 10-20x fewer samples. For example, we can estimate probability of harmful outputs on the order of 10^-4 with just 500 samples. Additionally, we find that these harmfulness estimates can reveal the sensitivity of models to perturbations in model input and predict deployment risks. Our work demonstrates that accurate rare-event estimation is both critical and feasible for safety evaluations. Code is available at https://github.com/rangell/LMTailRisk

Michael S. Albergo, Mark Goldstein, Nicholas M. Boffi et al.

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to \textit{couple} the base and the target densities, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does preclude) incorporating information about class labels or continuous embeddings. This enables us to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

Nihal Murali, Aahlad Puli, Ke Yu et al.

Deep Neural Networks (DNNs) are prone to learning spurious features that correlate with the label during training but are irrelevant to the learning problem. This hurts model generalization and poses problems when deploying them in safety-critical applications. This paper aims to better understand the effects of spurious features through the lens of the learning dynamics of the internal neurons during the training process. We make the following observations: (1) While previous works highlight the harmful effects of spurious features on the generalization ability of DNNs, we emphasize that not all spurious features are harmful. Spurious features can be "benign" or "harmful" depending on whether they are "harder" or "easier" to learn than the core features for a given model. This definition is model and dataset-dependent. (2) We build upon this premise and use instance difficulty methods (like Prediction Depth (Baldock et al., 2021)) to quantify "easiness" for a given model and to identify this behavior during the training phase. (3) We empirically show that the harmful spurious features can be detected by observing the learning dynamics of the DNN's early layers. In other words, easy features learned by the initial layers of a DNN early during the training can (potentially) hurt model generalization. We verify our claims on medical and vision datasets, both simulated and real, and justify the empirical success of our hypothesis by showing the theoretical connections between Prediction Depth and information-theoretic concepts like V-usable information (Ethayarajh et al., 2021). Lastly, our experiments show that monitoring only accuracy during training (as is common in machine learning pipelines) is insufficient to detect spurious features. We, therefore, highlight the need for monitoring early training dynamics using suitable instance difficulty metrics.

Neil Jethani, Adriel Saporta, Rajesh Ranganath

Feature attribution methods identify which features of an input most influence a model's output. Most widely-used feature attribution methods (such as SHAP, LIME, and Grad-CAM) are "class-dependent" methods in that they generate a feature attribution vector as a function of class. In this work, we demonstrate that class-dependent methods can "leak" information about the selected class, making that class appear more likely than it is. Thus, an end user runs the risk of drawing false conclusions when interpreting an explanation generated by a class-dependent method. In contrast, we introduce "distribution-aware" methods, which favor explanations that keep the label's distribution close to its distribution given all features of the input. We introduce SHAP-KL and FastSHAP-KL, two baseline distribution-aware methods that compute Shapley values. Finally, we perform a comprehensive evaluation of seven class-dependent and three distribution-aware methods on three clinical datasets of different high-dimensional data types: images, biosignals, and text.

Xintian Han, Mark Goldstein, Rajesh Ranganath

Survival analysis, the art of time-to-event modeling, plays an important role in clinical treatment decisions. Recently, continuous time models built from neural ODEs have been proposed for survival analysis. However, the training of neural ODEs is slow due to the high computational complexity of neural ODE solvers. Here, we propose an efficient alternative for flexible continuous time models, called Survival Mixture Density Networks (Survival MDNs). Survival MDN applies an invertible positive function to the output of Mixture Density Networks (MDNs). While MDNs produce flexible real-valued distributions, the invertible positive function maps the model into the time-domain while preserving a tractable density. Using four datasets, we show that Survival MDN performs better than, or similarly to continuous and discrete time baselines on concordance, integrated Brier score and integrated binomial log-likelihood. Meanwhile, Survival MDNs are also faster than ODE-based models and circumvent binning issues in discrete models.

Lily H. Zhang, Rajesh Ranganath

Methods which utilize the outputs or feature representations of predictive models have emerged as promising approaches for out-of-distribution (OOD) detection of image inputs. However, these methods struggle to detect OOD inputs that share nuisance values (e.g. background) with in-distribution inputs. The detection of shared-nuisance out-of-distribution (SN-OOD) inputs is particularly relevant in real-world applications, as anomalies and in-distribution inputs tend to be captured in the same settings during deployment. In this work, we provide a possible explanation for SN-OOD detection failures and propose nuisance-aware OOD detection to address them. Nuisance-aware OOD detection substitutes a classifier trained via empirical risk minimization and cross-entropy loss with one that 1. is trained under a distribution where the nuisance-label relationship is broken and 2. yields representations that are independent of the nuisance under this distribution, both marginally and conditioned on the label. We can train a classifier to achieve these objectives using Nuisance-Randomized Distillation (NuRD), an algorithm developed for OOD generalization under spurious correlations. Output- and feature-based nuisance-aware OOD detection perform substantially better than their original counterparts, succeeding even when detection based on domain generalization algorithms fails to improve performance.

Mukund Sudarshan, Aahlad Manas Puli, Wesley Tansey et al.

Conditional randomization tests (CRTs) assess whether a variable $x$ is predictive of another variable $y$, having observed covariates $z$. CRTs require fitting a large number of predictive models, which is often computationally intractable. Existing solutions to reduce the cost of CRTs typically split the dataset into a train and test portion, or rely on heuristics for interactions, both of which lead to a loss in power. We propose the decoupled independence test (DIET), an algorithm that avoids both of these issues by leveraging marginal independence statistics to test conditional independence relationships. DIET tests the marginal independence of two random variables: $F(x \mid z)$ and $F(y \mid z)$ where $F(\cdot \mid z)$ is a conditional cumulative distribution function (CDF). These variables are termed "information residuals." We give sufficient conditions for DIET to achieve finite sample type-1 error control and power greater than the type-1 error rate. We then prove that when using the mutual information between the information residuals as a test statistic, DIET yields the most powerful conditionally valid test. Finally, we show DIET achieves higher power than other tractable CRTs on several synthetic and real benchmarks.

Hao Zhang, Neil Jethani, Aahlad Puli et al.

Diabetes has a long asymptomatic period which can often remain undiagnosed for multiple years. In this study, we trained a deep learning model to detect new-onset diabetes using 12-lead ECG and readily available demographic information. To do so, we used retrospective data where patients have both a hemoglobin A1c and ECG measured. However, such patients may not be representative of the complete patient population. As part of the study, we proposed a methodology to evaluate our model in the target population by estimating the probability of receiving an A1c test and reweight the retrospective population to represent the general population. We also adapted an efficient algorithm to generate Shapley values for both ECG signals and demographic features at the same time for model interpretation. The model offers an automated, more accurate method for early diabetes detection compared to current screening efforts. Their potential use in wearable devices can facilitate large-scale, community-wide screening, improving healthcare outcomes.

Boyang Yu, Aakash Kaku, Kangning Liu et al.

Automatic assessment of impairment and disease severity is a key challenge in data-driven medicine. We propose a novel framework to address this challenge, which leverages AI models trained exclusively on healthy individuals. The COnfidence-Based chaRacterization of Anomalies (COBRA) score exploits the decrease in confidence of these models when presented with impaired or diseased patients to quantify their deviation from the healthy population. We applied the COBRA score to address a key limitation of current clinical evaluation of upper-body impairment in stroke patients. The gold-standard Fugl-Meyer Assessment (FMA) requires in-person administration by a trained assessor for 30-45 minutes, which restricts monitoring frequency and precludes physicians from adapting rehabilitation protocols to the progress of each patient. The COBRA score, computed automatically in under one minute, is shown to be strongly correlated with the FMA on an independent test cohort for two different data modalities: wearable sensors ($ρ= 0.845$, 95% CI [0.743,0.908]) and video ($ρ= 0.746$, 95% C.I [0.594, 0.847]). To demonstrate the generalizability of the approach to other conditions, the COBRA score was also applied to quantify severity of knee osteoarthritis from magnetic-resonance imaging scans, again achieving significant correlation with an independent clinical assessment ($ρ= 0.644$, 95% C.I [0.585,0.696]).

Raghav Singhal, Zachary Horvitz, Ryan Teehan et al.

Diffusion models produce impressive results in modalities ranging from images and video to protein design and text. However, generating samples with user-specified properties remains a challenge. Recent research proposes fine-tuning models to maximize rewards that capture desired properties, but these methods require expensive training and are prone to mode collapse. In this work, we present Feynman-Kac (FK) steering, an inference-time framework for steering diffusion models with reward functions. FK steering works by sampling a system of multiple interacting diffusion processes, called particles, and resampling particles at intermediate steps based on scores computed using functions called potentials. Potentials are defined using rewards for intermediate states and are selected such that a high value indicates that the particle will yield a high-reward sample. We explore various choices of potentials, intermediate rewards, and samplers. We evaluate FK steering on text-to-image and text diffusion models. For steering text-to-image models with a human preference reward, we find that FK steering a 0.8B parameter model outperforms a 2.6B parameter fine-tuned model on prompt fidelity, with faster sampling and no training. For steering text diffusion models with rewards for text quality and specific text attributes, we find that FK steering generates lower perplexity, more linguistically acceptable outputs and enables gradient-free control of attributes like toxicity. Our results demonstrate that inference-time scaling and steering of diffusion models - even with off-the-shelf rewards - can provide significant sample quality gains and controllability benefits. Code is available at https://github.com/zacharyhorvitz/Fk-Diffusion-Steering .

Raghav Singhal, Mark Goldstein, Rajesh Ranganath

Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a Gaussian stationary distribution. This limits the kinds of models that can be built to those that target a Gaussian prior or more generally limits the kinds of problems that can be generically solved to those that have conditionally linear score functions. In this work, we introduce a family of tractable denoising score matching objectives, called local-DSM, built using local increments of the diffusion process. We show how local-DSM melded with Taylor expansions enables automated training and score estimation with nonlinear diffusion processes. To demonstrate these ideas, we use automated-DSM to train generative models using non-Gaussian priors on challenging low dimensional distributions and the CIFAR10 image dataset. Additionally, we use the automated-DSM to learn the scores for nonlinear processes studied in statistical physics.

Donna Tjandra, Trenton Chang, Sonali Parbhoo et al.

Objective: The growing availability of large-scale observational clinical datasets and challenges in conducting randomized controlled trials have spurred enthusiasm in using causal machine learning (ML) for causal inference in observational data. We present a roadmap for applying causal ML to observational data. Materials and methods: We outline the importance of assessing validity assumptions within available data and applying causal ML responsibly for clinical experts using causal ML and ML practitioners with limited clinical expertise. Observations: Despite advances in causal ML, its limitations remain largely under-appreciated across disciplines. This gap in shared knowledge may impact the validity of findings. Discussion: Causal assumptions must be satisfied and modeling choices justified. Otherwise, these approaches risk producing biased or misleading results, with consequences for clinical research and patient care. Conclusion: Causal ML can be a powerful tool for generating causal hypotheses. We provide a template to strengthen the rigor and interpretability of causal analyses.

Adriel Saporta, Aahlad Puli, Mark Goldstein et al.

Contrastive learning methods, such as CLIP, leverage naturally paired data-for example, images and their corresponding text captions-to learn general representations that transfer efficiently to downstream tasks. While such approaches are generally applied to two modalities, domains such as robotics, healthcare, and video need to support many types of data at once. We show that the pairwise application of CLIP fails to capture joint information between modalities, thereby limiting the quality of the learned representations. To address this issue, we present Symile, a simple contrastive learning approach that captures higher-order information between any number of modalities. Symile provides a flexible, architecture-agnostic objective for learning modality-specific representations. To develop Symile's objective, we derive a lower bound on total correlation, and show that Symile representations for any set of modalities form a sufficient statistic for predicting the remaining modalities. Symile outperforms pairwise CLIP, even with modalities missing in the data, on cross-modal classification and retrieval across several experiments including on an original multilingual dataset of 33M image, text and audio samples and a clinical dataset of chest X-rays, electrocardiograms, and laboratory measurements. All datasets and code used in this work are publicly available at https://github.com/rajesh-lab/symile.

Jatin Prakash, Aahlad Puli, Rajesh Ranganath

The quadratic cost of attention in transformers motivated the development of efficient approaches: namely sparse and sliding window attention, convolutions and linear attention. Although these approaches result in impressive reductions in compute and memory, they often trade-off with quality, specifically in-context recall performance. Moreover, apriori fixing this quality-compute tradeoff means being suboptimal from the get-go: some downstream applications require more memory for in-context recall, while others require lower latency and memory. Further, these approaches rely on heuristic choices that artificially restrict attention, or require handcrafted and complex recurrent state update rules, or they must be carefully composed with attention at specific layers to form a hybrid architecture that complicates the design process, especially at scale. To address above issues, we propose Compress & Attend Transformer (CAT), a conceptually simple architecture employing two simple ingredients only: dense attention and compression. CAT decodes chunks of tokens by attending to compressed chunks of the sequence so far. Compression results in decoding from a reduced sequence length that yields compute and memory savings, while choosing a particular chunk size trades-off quality for efficiency. Moreover, CAT can be trained with multiple chunk sizes at once, unlocking control of quality-compute trade-offs directly at test-time without any retraining, all in a single adaptive architecture. In exhaustive evaluations on common language modeling tasks, in-context recall, and long-context understanding, a single adaptive CAT model outperforms existing efficient baselines, including hybrid architectures, across different compute-memory budgets. Further, a single CAT matches dense transformer in language modeling across model scales while being 1.4-3x faster and requiring 2-9x lower total memory usage.

Alp Kucukelbir, Rajesh Ranganath, Andrew Gelman et al.

Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult to automate. We propose an automatic variational inference algorithm, automatic differentiation variational inference (ADVI). The user only provides a Bayesian model and a dataset; nothing else. We make no conjugacy assumptions and support a broad class of models. The algorithm automatically determines an appropriate variational family and optimizes the variational objective. We implement ADVI in Stan (code available now), a probabilistic programming framework. We compare ADVI to MCMC sampling across hierarchical generalized linear models, nonconjugate matrix factorization, and a mixture model. We train the mixture model on a quarter million images. With ADVI we can use variational inference on any model we write in Stan.

Laura Manduchi, Clara Meister, Kushagra Pandey et al.

The field of deep generative modeling has grown rapidly in the last few years. With the availability of massive amounts of training data coupled with advances in scalable unsupervised learning paradigms, recent large-scale generative models show tremendous promise in synthesizing high-resolution images and text, as well as structured data such as videos and molecules. However, we argue that current large-scale generative AI models exhibit several fundamental shortcomings that hinder their widespread adoption across domains. In this work, our objective is to identify these issues and highlight key unresolved challenges in modern generative AI paradigms that should be addressed to further enhance their capabilities, versatility, and reliability. By identifying these challenges, we aim to provide researchers with insights for exploring fruitful research directions, thus fostering the development of more robust and accessible generative AI solutions.

Lucius E. J. Bynum, Aahlad Manas Puli, Diego Herrero-Quevedo et al.

Causal inference and the estimation of causal effects plays a central role in decision-making across many areas, including healthcare and economics. Estimating causal effects typically requires an estimator that is tailored to each problem of interest. But developing estimators can take significant effort for even a single causal inference setting. For example, algorithms for regression-based estimators, propensity score methods, and doubly robust methods were designed across several decades to handle causal estimation with observed confounders. Similarly, several estimators have been developed to exploit instrumental variables (IVs), including two-stage least-squares (TSLS), control functions, and the method-of-moments. In this work, we instead frame causal inference as a dataset-level prediction problem, offloading algorithm design to the learning process. The approach we introduce, called black box causal inference (BBCI), builds estimators in a black-box manner by learning to predict causal effects from sampled dataset-effect pairs. We demonstrate accurate estimation of average treatment effects (ATEs) and conditional average treatment effects (CATEs) with BBCI across several causal inference problems with known identification, including problems with less developed estimators.

Lily H. Zhang, Rajesh Ranganath

Preference learning, or the task of aligning generative models to preference comparison data, has yet to reach the conceptual maturity of classification, density estimation, etc. To close this gap, this work presents a framework to understand preference learning starting from the sampling distribution of pairwise preference data. First, we prove that the only evaluation of a generative model that respects both preferences and prevalences in the data distribution is a form of win rate, justifying win rate as the focal point to understand preference learning. We then analyze preference learning methods as win rate optimization (WRO) or non-WRO. We present novel instances of WRO beyond existing examples (RLHF, NLHF) and identify two key theoretical benefits of all such methods. We prove that common non-WRO methods like DPO and SFT on preferred samples lack these properties and suggest ways to mitigate such theoretical limitations. We also show that WRO underperforms in practice due optimization difficulties and that optimization success predicts performance better than choices which affect the objective's solution. Our analysis highlights best practices for existing methods and provides recommendations for future research, guided by the principle that one should either align non-WRO methods more closely with WRO or improve the optimization of WRO objectives.

Aahlad Puli, Nhi Nguyen, Rajesh Ranganath

Feature attributions attempt to highlight what inputs drive predictive power. Good attributions or explanations are thus those that produce inputs that retain this predictive power; accordingly, evaluations of explanations score their quality of prediction. However, evaluations produce scores better than what appears possible from the values in the explanation for a class of explanations, called encoding explanations. Probing for encoding remains a challenge because there is no general characterization of what gives the extra predictive power. We develop a definition of encoding that identifies this extra predictive power via conditional dependence and show that the definition fits existing examples of encoding. This definition implies, in contrast to encoding explanations, that non-encoding explanations contain all the informative inputs used to produce the explanation, giving them a "what you see is what you get" property, which makes them transparent and simple to use. Next, we prove that existing scores (ROAR, FRESH, EVAL-X) do not rank non-encoding explanations above encoding ones, and develop STRIPE-X which ranks them correctly. After empirically demonstrating the theoretical insights, we use STRIPE-X to show that despite prompting an LLM to produce non-encoding explanations for a sentiment analysis task, the LLM-generated explanations encode.

Anthony GX-Chen, Jatin Prakash, Jeff Guo et al.

It is commonly believed that optimizing the reverse KL divergence results in "mode seeking", while optimizing forward KL results in "mass covering", with the latter being preferred if the goal is to sample from multiple diverse modes. We show -- mathematically and empirically -- that this intuition does not necessarily transfer well to doing reinforcement learning with reverse/forward KL regularization (e.g. as commonly used with language models). Instead, the choice of reverse/forward KL determines the family of optimal target distributions, parameterized by the regularization coefficient. Mode coverage depends primarily on other factors, such as regularization strength, and relative scales between rewards and reference probabilities. Further, we show commonly used settings such as low regularization strength and equal verifiable rewards tend to specify unimodal target distributions, meaning the optimization objective is, by construction, non-diverse. We leverage these insights to construct a simple, scalable, and theoretically justified algorithm. It makes minimal changes to reward magnitudes, yet optimizes for a target distribution which puts high probability over all high-quality sampling modes. In experiments, this simple modification works to post-train both Large Language Models and Chemical Language Models to have higher solution quality and diversity, without any external signals of diversity, and works with both forward and reverse KL when using either naively fails.

Zachary Horvitz, Raghav Singhal, Hao Zou et al.

Masked diffusion language models (MDLMs) are trained to in-fill positions in randomly masked sequences, in contrast to next-token prediction models. Discussions around MDLMs focus on two benefits: (1) any-order decoding and 2) multi-token decoding. However, we observe that for math and coding tasks, any-order algorithms often underperform or behave similarly to left-to-right sampling, and standard multi-token decoding significantly degrades performance. At inference time, MDLMs compute the conditional distribution of all masked positions. A natural question is: How can we justify this additional compute when left-to-right one-token-at-a-time decoding is on par with any-order decoding algorithms? First, we propose reasoning-as-infilling. By using MDLMs to infill a reasoning template, we can structure outputs and distinguish between reasoning and answer tokens. In turn, this enables measuring answer uncertainty during reasoning, and early exits when the model converges on an answer. Next, given an answer, reasoning-as-infilling enables sampling from the MDLM posterior over reasoning traces conditioned on the answer, providing a new source of high-quality data for post-training. On GSM8k, we observe that fine-tuning LLaDA-8B Base on its posterior reasoning traces provides a performance boost on par with fine-tuning on human-written reasoning traces. Additionally, given an answer, reasoning-as-infilling provides a method for scoring the correctness of the reasoning process at intermediate steps. Second, we propose multi-token entropy decoding (MED), a simple adaptive sampler that minimizes the error incurred by decoding positions in parallel based on the conditional entropies of those positions. MED preserves performance across benchmarks and leads to 2.7x fewer steps. Our work demonstrates that the training and compute used by MDLMs unlock many new inference and post-training methods.

Shiye Su, Yuhui Zhang, Linqi Zhou et al. · stanford

Modeling transformations between arbitrary data distributions is a fundamental scientific challenge, arising in applications like drug discovery and evolutionary simulation. While flow matching offers a natural framework for this task, its use has thus far primarily focused on the noise-to-data setting, while its application in the general distribution-to-distribution setting is underexplored. We find that in the latter case, where the source is also a data distribution to be learned from limited samples, standard flow matching fails due to sparse supervision. To address this, we propose a simple and computationally efficient method that injects stochasticity into the training process by perturbing source samples and flow interpolants. On five diverse imaging tasks spanning biology, radiology, and astronomy, our method significantly improves generation quality, outperforming existing baselines by an average of 9 FID points. Our approach also reduces the transport cost between input and generated samples to better highlight the true effect of the transformation, making flow matching a more practical tool for simulating the diverse distribution transformations that arise in science.

Yoav Wald, Mark Goldstein, Yonathan Efroni et al.

Problems in fields such as healthcare, robotics, and finance requires reasoning about the value both of what decision or action to take and when to take it. The prevailing hope is that artificial intelligence will support such decisions by estimating the causal effect of policies such as how to treat patients or how to allocate resources over time. However, existing methods for estimating the effect of a policy struggle with \emph{irregular time}. They either discretize time, or disregard the effect of timing policies. We present a new deep-Q algorithm that estimates the effect of both when and what to do called Earliest Disagreement Q-Evaluation (EDQ). EDQ makes use of recursion for the Q-function that is compatible with flexible sequence models, such as transformers. EDQ provides accurate estimates under standard assumptions. We validate the approach through experiments on survival time and tumor growth tasks.

Lily H. Zhang, Rajesh Ranganath, Arya Tafvizi

Generative models of language exhibit impressive capabilities but still place non-negligible probability mass over undesirable outputs. In this work, we address the task of updating a model to avoid unwanted outputs while minimally changing model behavior otherwise, a challenge we refer to as a minimal targeted update. We first formalize the notion of a minimal targeted update and propose a method to achieve such updates using negative examples from a model's generations. Our proposed Targeted Negative Training (TNT) results in updates that keep the new distribution close to the original, unlike existing losses for negative signal which push down probability but do not control what the updated distribution will be. In experiments, we demonstrate that TNT yields a better trade-off between reducing unwanted behavior and maintaining model generation behavior than baselines, paving the way towards a modeling paradigm based on iterative training updates that constrain models from generating undesirable outputs while preserving their impressive capabilities.

Chen-Yu Yen, Raghav Singhal, Umang Sharma et al.

Magnetic Resonance (MR) imaging, despite its proven diagnostic utility, remains an inaccessible imaging modality for disease surveillance at the population level. A major factor rendering MR inaccessible is lengthy scan times. An MR scanner collects measurements associated with the underlying anatomy in the Fourier space, also known as the k-space. Creating a high-fidelity image requires collecting large quantities of such measurements, increasing the scan time. Traditionally to accelerate an MR scan, image reconstruction from under-sampled k-space data is the method of choice. However, recent works show the feasibility of bypassing image reconstruction and directly learning to detect disease directly from a sparser learned subset of the k-space measurements. In this work, we propose Adaptive Sampling for MR (ASMR), a sampling method that learns an adaptive policy to sequentially select k-space samples to optimize for target disease detection. On 6 out of 8 pathology classification tasks spanning the Knee, Brain, and Prostate MR scans, ASMR reaches within 2% of the performance of a fully sampled classifier while using only 8% of the k-space, as well as outperforming prior state-of-the-art work in k-space sampling such as EMRT, LOUPE, and DPS.

Abhijith Gandrakota, Lily Zhang, Aahlad Puli et al.

Anomaly, or out-of-distribution, detection is a promising tool for aiding discoveries of new particles or processes in particle physics. In this work, we identify and address two overlooked opportunities to improve anomaly detection for high-energy physics. First, rather than train a generative model on the single most dominant background process, we build detection algorithms using representation learning from multiple background types, thus taking advantage of more information to improve estimation of what is relevant for detection. Second, we generalize decorrelation to the multi-background setting, thus directly enforcing a more complete definition of robustness for anomaly detection. We demonstrate the benefit of the proposed robust multi-background anomaly detection algorithms on a high-dimensional dataset of particle decays at the Large Hadron Collider.

David Brandfonbrener, William F. Whitney, Rajesh Ranganath et al.

We introduce quantile filtered imitation learning (QFIL), a novel policy improvement operator designed for offline reinforcement learning. QFIL performs policy improvement by running imitation learning on a filtered version of the offline dataset. The filtering process removes $ s,a $ pairs whose estimated Q values fall below a given quantile of the pushforward distribution over values induced by sampling actions from the behavior policy. The definitions of both the pushforward Q distribution and resulting value function quantile are key contributions of our method. We prove that QFIL gives us a safe policy improvement step with function approximation and that the choice of quantile provides a natural hyperparameter to trade off bias and variance of the improvement step. Empirically, we perform a synthetic experiment illustrating how QFIL effectively makes a bias-variance tradeoff and we see that QFIL performs well on the D4RL benchmark.

Mark Goldstein, Jörn-Henrik Jacobsen, Olina Chau et al.

Spurious correlations allow flexible models to predict well during training but poorly on related test distributions. Recent work has shown that models that satisfy particular independencies involving correlation-inducing \textit{nuisance} variables have guarantees on their test performance. Enforcing such independencies requires nuisances to be observed during training. However, nuisances, such as demographics or image background labels, are often missing. Enforcing independence on just the observed data does not imply independence on the entire population. Here we derive \acrshort{mmd} estimators used for invariance objectives under missing nuisances. On simulations and clinical data, optimizing through these estimates achieves test performance similar to using estimators that make use of the full data.

Xintian Han, Mark Goldstein, Aahlad Puli et al.

Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution. However, estimating the censoring model under these metrics requires inverse-weighting by the failure distribution. The objective for each model requires the other, but neither are known. To resolve this dilemma, we introduce Inverse-Weighted Survival Games. In these games, objectives for each model are built from re-weighted estimates featuring the other model, where the latter is held fixed during training. When the loss is proper, we show that the games always have the true failure and censoring distributions as a stationary point. This means models in the game do not leave the correct distributions once reached. We construct one case where this stationary point is unique. We show that these games optimize BS on simulations and then apply these principles on real world cancer and critically-ill patient data.

Neil Jethani, Mukund Sudarshan, Ian Covert et al.

Shapley values are widely used to explain black-box models, but they are costly to calculate because they require many model evaluations. We introduce FastSHAP, a method for estimating Shapley values in a single forward pass using a learned explainer model. FastSHAP amortizes the cost of explaining many inputs via a learning approach inspired by the Shapley value's weighted least squares characterization, and it can be trained using standard stochastic gradient optimization. We compare FastSHAP to existing estimation approaches, revealing that it generates high-quality explanations with orders of magnitude speedup.

Lily H. Zhang, Mark Goldstein, Rajesh Ranganath

Deep generative models (DGMs) seem a natural fit for detecting out-of-distribution (OOD) inputs, but such models have been shown to assign higher probabilities or densities to OOD images than images from the training distribution. In this work, we explain why this behavior should be attributed to model misestimation. We first prove that no method can guarantee performance beyond random chance without assumptions on which out-distributions are relevant. We then interrogate the typical set hypothesis, the claim that relevant out-distributions can lie in high likelihood regions of the data distribution, and that OOD detection should be defined based on the data distribution's typical set. We highlight the consequences implied by assuming support overlap between in- and out-distributions, as well as the arbitrariness of the typical set for OOD detection. Our results suggest that estimation error is a more plausible explanation than the misalignment between likelihood-based OOD detection and out-distributions of interest, and we illustrate how even minimal estimation error can lead to OOD detection failures, yielding implications for future work in deep generative modeling and OOD detection.

Aahlad Puli, Lily H. Zhang, Eric K. Oermann et al.

In many prediction problems, spurious correlations are induced by a changing relationship between the label and a nuisance variable that is also correlated with the covariates. For example, in classifying animals in natural images, the background, which is a nuisance, can predict the type of animal. This nuisance-label relationship does not always hold, and the performance of a model trained under one such relationship may be poor on data with a different nuisance-label relationship. To build predictive models that perform well regardless of the nuisance-label relationship, we develop Nuisance-Randomized Distillation (NURD). We introduce the nuisance-randomized distribution, a distribution where the nuisance and the label are independent. Under this distribution, we define the set of representations such that conditioning on any member, the nuisance and the label remain independent. We prove that the representations in this set always perform better than chance, while representations outside of this set may not. NURD finds a representation from this set that is most informative of the label under the nuisance-randomized distribution, and we prove that this representation achieves the highest performance regardless of the nuisance-label relationship. We evaluate NURD on several tasks including chest X-ray classification where, using non-lung patches as the nuisance, NURD produces models that predict pneumonia under strong spurious correlations.

David Brandfonbrener, William F. Whitney, Rajesh Ranganath et al.

Most prior approaches to offline reinforcement learning (RL) have taken an iterative actor-critic approach involving off-policy evaluation. In this paper we show that simply doing one step of constrained/regularized policy improvement using an on-policy Q estimate of the behavior policy performs surprisingly well. This one-step algorithm beats the previously reported results of iterative algorithms on a large portion of the D4RL benchmark. The one-step baseline achieves this strong performance while being notably simpler and more robust to hyperparameters than previously proposed iterative algorithms. We argue that the relatively poor performance of iterative approaches is a result of the high variance inherent in doing off-policy evaluation and magnified by the repeated optimization of policies against those estimates. In addition, we hypothesize that the strong performance of the one-step algorithm is due to a combination of favorable structure in the environment and behavior policy.

Neil Jethani, Mukund Sudarshan, Yindalon Aphinyanaphongs et al.

While the need for interpretable machine learning has been established, many common approaches are slow, lack fidelity, or hard to evaluate. Amortized explanation methods reduce the cost of providing interpretations by learning a global selector model that returns feature importances for a single instance of data. The selector model is trained to optimize the fidelity of the interpretations, as evaluated by a predictor model for the target. Popular methods learn the selector and predictor model in concert, which we show allows predictions to be encoded within interpretations. We introduce EVAL-X as a method to quantitatively evaluate interpretations and REAL-X as an amortized explanation method, which learn a predictor model that approximates the true data generating distribution given any subset of the input. We show EVAL-X can detect when predictions are encoded in interpretations and show the advantages of REAL-X through quantitative and radiologist evaluation.

Aahlad Puli, Adler J. Perotte, Rajesh Ranganath

Causal inference relies on two fundamental assumptions: ignorability and positivity. We study causal inference when the true confounder value can be expressed as a function of the observed data; we call this setting estimation with functional confounders (EFC). In this setting, ignorability is satisfied, however positivity is violated, and causal inference is impossible in general. We consider two scenarios where causal effects are estimable. First, we discuss interventions on a part of the treatment called functional interventions and a sufficient condition for effect estimation of these interventions called functional positivity. Second, we develop conditions for nonparametric effect estimation based on the gradient fields of the functional confounder and the true outcome function. To estimate effects under these conditions, we develop Level-set Orthogonal Descent Estimation (LODE). Further, we prove error bounds on LODE's effect estimates, evaluate our methods on simulated and real data, and empirically demonstrate the value of EFC.

Mark Goldstein, Xintian Han, Aahlad Puli et al.

Survival analysis models the distribution of time until an event of interest, such as discharge from the hospital or admission to the ICU. When a model's predicted number of events within any time interval is similar to the observed number, it is called well-calibrated. A survival model's calibration can be measured using, for instance, distributional calibration (D-CALIBRATION) [Haider et al., 2020] which computes the squared difference between the observed and predicted number of events within different time intervals. Classically, calibration is addressed in post-training analysis. We develop explicit calibration (X-CAL), which turns D-CALIBRATION into a differentiable objective that can be used in survival modeling alongside maximum likelihood estimation and other objectives. X-CAL allows practitioners to directly optimize calibration and strike a desired balance between predictive power and calibration. In our experiments, we fit a variety of shallow and deep models on simulated data, a survival dataset based on MNIST, on length-of-stay prediction using MIMIC-III data, and on brain cancer data from The Cancer Genome Atlas. We show that the models we study can be miscalibrated. We give experimental evidence on these datasets that X-CAL improves D-CALIBRATION without a large decrease in concordance or likelihood.

Irene Y. Chen, Shalmali Joshi, Marzyeh Ghassemi et al.

Machine learning can be used to make sense of healthcare data. Probabilistic machine learning models help provide a complete picture of observed data in healthcare. In this review, we examine how probabilistic machine learning can advance healthcare. We consider challenges in the predictive model building pipeline where probabilistic models can be beneficial including calibration and missing data. Beyond predictive models, we also investigate the utility of probabilistic machine learning models in phenotyping, in generative models for clinical use cases, and in reinforcement learning.

Mukund Sudarshan, Wesley Tansey, Rajesh Ranganath

Predictive modeling often uses black box machine learning methods, such as deep neural networks, to achieve state-of-the-art performance. In scientific domains, the scientist often wishes to discover which features are actually important for making the predictions. These discoveries may lead to costly follow-up experiments and as such it is important that the error rate on discoveries is not too high. Model-X knockoffs enable important features to be discovered with control of the FDR. However, knockoffs require rich generative models capable of accurately modeling the knockoff features while ensuring they obey the so-called "swap" property. We develop Deep Direct Likelihood Knockoffs (DDLK), which directly minimizes the KL divergence implied by the knockoff swap property. DDLK consists of two stages: it first maximizes the explicit likelihood of the features, then minimizes the KL divergence between the joint distribution of features and knockoffs and any swap between them. To ensure that the generated knockoffs are valid under any possible swap, DDLK uses the Gumbel-Softmax trick to optimize the knockoff generator under the worst-case swap. We find DDLK has higher power than baselines while controlling the false discovery rate on a variety of synthetic and real benchmarks including a task involving a large dataset from one of the epicenters of COVID-19.

David Brandfonbrener, William F. Whitney, Rajesh Ranganath et al.

Recent results in supervised learning suggest that while overparameterized models have the capacity to overfit, they in fact generalize quite well. We ask whether the same phenomenon occurs for offline contextual bandits. Our results are mixed. Value-based algorithms benefit from the same generalization behavior as overparameterized supervised learning, but policy-based algorithms do not. We show that this discrepancy is due to the \emph{action-stability} of their objectives. An objective is action-stable if there exists a prediction (action-value vector or action distribution) which is optimal no matter which action is observed. While value-based objectives are action-stable, policy-based objectives are unstable. We formally prove upper bounds on the regret of overparameterized value-based learning and lower bounds on the regret for policy-based algorithms. In our experiments with large neural networks, this gap between action-stable value-based objectives and unstable policy-based objectives leads to significant performance differences.

Amelia J. Averitt, Natnicha Vanitchanant, Rajesh Ranganath et al.

Causal inference often relies on the counterfactual framework, which requires that treatment assignment is independent of the outcome, known as strong ignorability. Approaches to enforcing strong ignorability in causal analyses of observational data include weighting and matching methods. Effect estimates, such as the average treatment effect (ATE), are then estimated as expectations under the reweighted or matched distribution, P . The choice of P is important and can impact the interpretation of the effect estimate and the variance of effect estimates. In this work, instead of specifying P, we learn a distribution that simultaneously maximizes coverage and minimizes variance of ATE estimates. In order to learn this distribution, this research proposes a generative adversarial network (GAN)-based model called the Counterfactual $χ$-GAN (cGAN), which also learns feature-balancing weights and supports unbiased causal estimation in the absence of unobserved confounding. Our model minimizes the Pearson $χ^2$ divergence, which we show simultaneously maximizes coverage and minimizes the variance of importance sampling estimates. To our knowledge, this is the first such application of the Pearson $χ^2$ divergence. We demonstrate the effectiveness of cGAN in achieving feature balance relative to established weighting methods in simulation and with real-world medical data.

Dieterich Lawson, George Tucker, Bo Dai et al.

Energy-based models (EBMs) are powerful probabilistic models, but suffer from intractable sampling and density evaluation due to the partition function. As a result, inference in EBMs relies on approximate sampling algorithms, leading to a mismatch between the model and inference. Motivated by this, we consider the sampler-induced distribution as the model of interest and maximize the likelihood of this model. This yields a class of energy-inspired models (EIMs) that incorporate learned energy functions while still providing exact samples and tractable log-likelihood lower bounds. We describe and evaluate three instantiations of such models based on truncated rejection sampling, self-normalized importance sampling, and Hamiltonian importance sampling. These models outperform or perform comparably to the recently proposed Learned Accept/Reject Sampling algorithm and provide new insights on ranking Noise Contrastive Estimation and Contrastive Predictive Coding. Moreover, EIMs allow us to generalize a recent connection between multi-sample variational lower bounds and auxiliary variable variational inference. We show how recent variational bounds can be unified with EIMs as the variational family.