Benjamin Lengerich

Benjamin Lengerich, Caleb N. Ellington, Andrea Rubbi et al.

We examine Contextualized Machine Learning (ML), a paradigm for learning heterogeneous and context-dependent effects. Contextualized ML estimates heterogeneous functions by applying deep learning to the meta-relationship between contextual information and context-specific parametric models. This is a form of varying-coefficient modeling that unifies existing frameworks including cluster analysis and cohort modeling by introducing two reusable concepts: a context encoder which translates sample context into model parameters, and sample-specific model which operates on sample predictors. We review the process of developing contextualized models, nonparametric inference from contextualized models, and identifiability conditions of contextualized models. Finally, we present the open-source PyTorch package ContextualizedML.

Dong Liu, Yanxuan Yu, Yite Wang et al.

This paper focuses on modern efficient training and inference technologies on foundation models and illustrates them from two perspectives: model and system design. Model and System Design optimize LLM training and inference from different aspects to save computational resources, making LLMs more efficient, affordable, and more accessible. The paper list repository is available at https://github.com/NoakLiu/Efficient-Foundation-Models-Survey.

Benjamin Lengerich, Mark E. Nunnally, Yin Aphinyanaphongs et al.

Treatment protocols, disease understanding, and viral characteristics changed over the course of the COVID-19 pandemic; as a result, the risks associated with patient comorbidities and biomarkers also changed. We add to the conversation regarding inflammation, hemostasis and vascular function in COVID-19 by performing a time-varying observational analysis of over 4000 patients hospitalized for COVID-19 in a New York City hospital system from March 2020 to August 2021. To perform this analysis, we apply tree-based generalized additive models with temporal interactions which recover discontinuous risk changes caused by discrete protocols changes. We find that the biomarkers of thrombosis increasingly predicted mortality from March 2020 to August 2021, while the association between biomarkers of inflammation and thrombosis weakened. Beyond COVID-19, this presents a straightforward methodology to estimate unknown and discontinuous time-varying effects.

Benjamin Lengerich, Eric P. Xing, Rich Caruana

We examine Dropout through the perspective of interactions. This view provides a symmetry to explain Dropout: given $N$ variables, there are ${N \choose k}$ possible sets of $k$ variables to form an interaction (i.e. $\mathcal{O}(N^k)$); conversely, the probability an interaction of $k$ variables survives Dropout at rate $p$ is $(1-p)^k$ (decaying with $k$). These rates effectively cancel, and so Dropout regularizes against higher-order interactions. We prove this perspective analytically and empirically. This perspective of Dropout as a regularizer against interaction effects has several practical implications: (1) higher Dropout rates should be used when we need stronger regularization against spurious high-order interactions, (2) caution should be exercised when interpreting Dropout-based explanations and uncertainty measures, and (3) networks trained with Input Dropout are biased estimators. We also compare Dropout to other regularizers and find that it is difficult to obtain the same selective pressure against high-order interactions.

Benjamin Lengerich, Sarah Tan, Chun-Hao Chang et al.

Models which estimate main effects of individual variables alongside interaction effects have an identifiability challenge: effects can be freely moved between main effects and interaction effects without changing the model prediction. This is a critical problem for interpretability because it permits "contradictory" models to represent the same function. To solve this problem, we propose pure interaction effects: variance in the outcome which cannot be represented by any smaller subset of features. This definition has an equivalence with the Functional ANOVA decomposition. To compute this decomposition, we present a fast, exact algorithm that transforms any piecewise-constant function (such as a tree-based model) into a purified, canonical representation. We apply this algorithm to Generalized Additive Models with interactions trained on several datasets and show large disparity, including contradictions, between the effects before and after purification. These results underscore the need to specify data distributions and ensure identifiability before interpreting model parameters.

Benjamin Lengerich, Bryon Aragam, Eric P. Xing

Modern applications of machine learning (ML) deal with increasingly heterogeneous datasets comprised of data collected from overlapping latent subpopulations. As a result, traditional models trained over large datasets may fail to recognize highly predictive localized effects in favour of weakly predictive global patterns. This is a problem because localized effects are critical to developing individualized policies and treatment plans in applications ranging from precision medicine to advertising. To address this challenge, we propose to estimate sample-specific models that tailor inference and prediction at the individual level. In contrast to classical ML models that estimate a single, complex model (or only a few complex models), our approach produces a model personalized to each sample. These sample-specific models can be studied to understand subgroup dynamics that go beyond coarse-grained class labels. Crucially, our approach does not assume that relationships between samples (e.g. a similarity network) are known a priori. Instead, we use unmodeled covariates to learn a latent distance metric over the samples. We apply this approach to financial, biomedical, and electoral data as well as simulated data and show that sample-specific models provide fine-grained interpretations of complicated phenomena without sacrificing predictive accuracy compared to state-of-the-art models such as deep neural networks.