Andrew Warrington

Jimmy T. H. Smith, Andrew Warrington, Scott W. Linderman

Models using structured state space sequence (S4) layers have achieved state-of-the-art performance on long-range sequence modeling tasks. An S4 layer combines linear state space models (SSMs), the HiPPO framework, and deep learning to achieve high performance. We build on the design of the S4 layer and introduce a new state space layer, the S5 layer. Whereas an S4 layer uses many independent single-input, single-output SSMs, the S5 layer uses one multi-input, multi-output SSM. We establish a connection between S5 and S4, and use this to develop the initialization and parameterization used by the S5 model. The result is a state space layer that can leverage efficient and widely implemented parallel scans, allowing S5 to match the computational efficiency of S4, while also achieving state-of-the-art performance on several long-range sequence modeling tasks. S5 averages 87.4% on the long range arena benchmark, and 98.5% on the most difficult Path-X task.

Xavier Gonzalez, Andrew Warrington, Jimmy T. H. Smith et al.

Transformers and linear state space models can be evaluated in parallel on modern hardware, but evaluating nonlinear RNNs appears to be an inherently sequential problem. Recently, however, Lim et al. '24 developed an approach called DEER, which evaluates nonlinear RNNs in parallel by posing the states as the solution to a fixed-point problem. They derived a parallel form of Newton's method to solve the fixed-point problem and achieved significant speedups over sequential evaluation. However, the computational complexity of DEER is cubic in the state size, and the algorithm can suffer from numerical instability. We address these limitations with two novel contributions. To reduce the computational complexity, we apply quasi-Newton approximations and show they converge comparably to Newton, use less memory, and are faster. To stabilize DEER, we leverage a connection between the Levenberg-Marquardt algorithm and Kalman smoothing, which we call ELK. This connection allows us to stabilize Newton's method while using efficient parallelized Kalman smoothing algorithms to retain performance. Through several experiments, we show that these innovations allow for parallel evaluation of nonlinear RNNs at larger scales and with greater stability.

Dieterich Lawson, Allan Raventós, Andrew Warrington et al.

Sequential Monte Carlo (SMC) is an inference algorithm for state space models that approximates the posterior by sampling from a sequence of target distributions. The target distributions are often chosen to be the filtering distributions, but these ignore information from future observations, leading to practical and theoretical limitations in inference and model learning. We introduce SIXO, a method that instead learns targets that approximate the smoothing distributions, incorporating information from all observations. The key idea is to use density ratio estimation to fit functions that warp the filtering distributions into the smoothing distributions. We then use SMC with these learned targets to define a variational objective for model and proposal learning. SIXO yields provably tighter log marginal lower bounds and offers significantly more accurate posterior inferences and parameter estimates in a variety of domains.

Hyun Dong Lee, Andrew Warrington, Joshua I. Glaser et al.

An important problem in time-series analysis is modeling systems with time-varying dynamics. Probabilistic models with joint continuous and discrete latent states offer interpretable, efficient, and experimentally useful descriptions of such data. Commonly used models include autoregressive hidden Markov models (ARHMMs) and switching linear dynamical systems (SLDSs), each with its own advantages and disadvantages. ARHMMs permit exact inference and easy parameter estimation, but are parameter intensive when modeling long dependencies, and hence are prone to overfitting. In contrast, SLDSs can capture long-range dependencies in a parameter efficient way through Markovian latent dynamics, but present an intractable likelihood and a challenging parameter estimation task. In this paper, we propose switching autoregressive low-rank tensor (SALT) models, which retain the advantages of both approaches while ameliorating the weaknesses. SALT parameterizes the tensor of an ARHMM with a low-rank factorization to control the number of parameters and allow longer range dependencies without overfitting. We prove theoretical and discuss practical connections between SALT, linear dynamical systems, and SLDSs. We empirically demonstrate quantitative advantages of SALT models on a range of simulated and real prediction tasks, including behavioral and neural datasets. Furthermore, the learned low-rank tensor provides novel insights into temporal dependencies within each discrete state.

Alex Boyd, Andrew Warrington, Taha Kass-Hout et al.

Foundational marked temporal point process (MTPP) models, such as the Hawkes process, often use inexpressive model families in order to offer interpretable parameterizations of event data. On the other hand, neural MTPPs models forego this interpretability in favor of absolute predictive performance. In this work, we present a new family MTPP models: the hyper Hawkes process (HHP), which aims to be as flexible and performant as neural MTPPs, while retaining interpretable aspects. To achieve this, the HHP extends the classical Hawkes process to increase its expressivity by first expanding the dimension of the process into a latent space, and then introducing a hypernetwork to allow time- and data-dependent dynamics. These extensions define a highly performant MTPP family, achieving state-of-the-art performance across a range of benchmark tasks and metrics. Furthermore, by retaining the linearity of the recurrence, albeit now piecewise and conditionally linear, the HHP also retains much of the structure of the original Hawkes process, which we exploit to create direct probes into how the model creates predictions. HHP models therefore offer both state-of-the-art predictions, while also providing an opportunity to ``open the box'' and inspect how predictions were generated.

Yuxin Chang, Alex Boyd, Cao Xiao et al.

Marked temporal point processes (MTPPs) model sequences of events occurring at irregular time intervals, with wide-ranging applications in fields such as healthcare, finance and social networks. We propose the state-space point process (S2P2) model, a novel and performant model that leverages techniques derived for modern deep state-space models (SSMs) to overcome limitations of existing MTPP models, while simultaneously imbuing strong inductive biases for continuous-time event sequences that other discrete sequence models (i.e., RNNs, transformers) do not capture. Inspired by the classical linear Hawkes processes, we propose an architecture that interleaves stochastic jump differential equations with nonlinearities to create a highly expressive intensity-based MTPP model, without the need for restrictive parametric assumptions for the intensity. Our approach enables efficient training and inference with a parallel scan, bringing linear complexity and sublinear scaling while retaining expressivity to MTPPs. Empirically, S2P2 achieves state-of-the-art predictive likelihoods across eight real-world datasets, delivering an average improvement of 33% over the best existing approaches.

Fridolin Haugg, Grace Lee, John He et al.

Background: Facial appearance offers a noninvasive window into health. We built FAHR-Face, a foundation model trained on >40 million facial images and fine-tuned it for two distinct tasks: biological age estimation (FAHR-FaceAge) and survival risk prediction (FAHR-FaceSurvival). Methods: FAHR-FaceAge underwent a two-stage, age-balanced fine-tuning on 749,935 public images; FAHR-FaceSurvival was fine-tuned on 34,389 photos of cancer patients. Model robustness (cosmetic surgery, makeup, pose, lighting) and independence (saliency mapping) was tested extensively. Both models were clinically tested in two independent cancer patient datasets with survival analyzed by multivariable Cox models and adjusted for clinical prognostic factors. Findings: For age estimation, FAHR-FaceAge had the lowest mean absolute error of 5.1 years on public datasets, outperforming benchmark models and maintaining accuracy across the full human lifespan. In cancer patients, FAHR-FaceAge outperformed a prior facial age estimation model in survival prognostication. FAHR-FaceSurvival demonstrated robust prediction of mortality, and the highest-risk quartile had more than triple the mortality of the lowest (adjusted hazard ratio 3.22; P<0.001). These findings were validated in the independent cohort and both models showed generalizability across age, sex, race and cancer subgroups. The two algorithms provided distinct, complementary prognostic information; saliency mapping revealed each model relied on distinct facial regions. The combination of FAHR-FaceAge and FAHR-FaceSurvival improved prognostic accuracy. Interpretation: A single foundation model can generate inexpensive, scalable facial biomarkers that capture both biological ageing and disease-related mortality risk. The foundation model enabled effective training using relatively small clinical datasets.

Andrew Warrington, J. Wilder Lavington, Adam Ścibior et al.

Policies for partially observed Markov decision processes can be efficiently learned by imitating policies for the corresponding fully observed Markov decision processes. Unfortunately, existing approaches for this kind of imitation learning have a serious flaw: the expert does not know what the trainee cannot see, and so may encourage actions that are sub-optimal, even unsafe, under partial information. We derive an objective to instead train the expert to maximize the expected reward of the imitating agent policy, and use it to construct an efficient algorithm, adaptive asymmetric DAgger (A2D), that jointly trains the expert and the agent. We show that A2D produces an expert policy that the agent can safely imitate, in turn outperforming policies learned by imitating a fixed expert.

Frank Wood, Andrew Warrington, Saeid Naderiparizi et al.

In this work we demonstrate how to automate parts of the infectious disease-control policy-making process via performing inference in existing epidemiological models. The kind of inference tasks undertaken include computing the posterior distribution over controllable, via direct policy-making choices, simulation model parameters that give rise to acceptable disease progression outcomes. Among other things, we illustrate the use of a probabilistic programming language that automates inference in existing simulators. Neither the full capabilities of this tool for automating inference nor its utility for planning is widely disseminated at the current time. Timely gains in understanding about how such simulation-based models and inference automation tools applied in support of policymaking could lead to less economically damaging policy prescriptions, particularly during the current COVID-19 pandemic.

Andrew Warrington, Saeid Naderiparizi, Frank Wood

Deterministic models are approximations of reality that are easy to interpret and often easier to build than stochastic alternatives. Unfortunately, as nature is capricious, observational data can never be fully explained by deterministic models in practice. Observation and process noise need to be added to adapt deterministic models to behave stochastically, such that they are capable of explaining and extrapolating from noisy data. We investigate and address computational inefficiencies that arise from adding process noise to deterministic simulators that fail to return for certain inputs; a property we describe as "brittle." We show how to train a conditional normalizing flow to propose perturbations such that the simulator succeeds with high probability, increasing computational efficiency.

Andrew Warrington, Arthur Spencer, Frank Wood

We develop a stochastic whole-brain and body simulator of the nematode roundworm Caenorhabditis elegans (C. elegans) and show that it is sufficiently regularizing to allow imputation of latent membrane potentials from partial calcium fluorescence imaging observations. This is the first attempt we know of to "complete the circle," where an anatomically grounded whole-connectome simulator is used to impute a time-varying "brain" state at single-cell fidelity from covariates that are measurable in practice. The sequential Monte Carlo (SMC) method we employ not only enables imputation of said latent states but also presents a strategy for learning simulator parameters via variational optimization of the noisy model evidence approximation provided by SMC. Our imputation and parameter estimation experiments were conducted on distributed systems using novel implementations of the aforementioned techniques applied to synthetic data of dimension and type representative of that which are measured in laboratories currently.

Andrew Warrington, Neil Dhir

We present an instance of the optimal sensor scheduling problem with the additional relaxation that our observer makes active choices whether or not to observe and how to observe. We mask the nodes in a directed acyclic graph of the model that are observable, effectively optimising whether or not an observation should be made at each time step. The reason for this is simple: it is prudent to seek to reduce sensor costs, since resources (e.g. hardware, personnel and time) are finite. Consequently, rather than treating our plant as if it had infinite sensing resources, we seek to jointly maximise the utility of each perception. This reduces resource expenditure by explicitly minimising an observation-associated cost (e.g. battery use) while also facilitating the potential to yield better state estimates by virtue of being able to use more perceptions in noisy or unpredictable regions of state-space (e.g. a busy traffic junction). We present a general formalisation and notation of this problem, capable of encompassing much of the prior art. To illustrate our formulation, we pose and solve two example problems in this domain. Finally we suggest active areas of research to improve and further generalise this approach.

Andrew Warrington, Frank Wood

We present an updated version of the VESICLE-CNN algorithm presented by Roncal et al. (2014). The original implementation makes use of a patch-based approach. This methodology is known to be slow due to repeated computations. We update this implementation to be fully convolutional through the use of dilated convolutions, recovering the expanded field of view achieved through the use of strided maxpools, but without a degradation of spatial resolution. This updated implementation performs as well as the original implementation, but with a $600\times$ speedup at test time. We release source code and data into the public domain.

Tom Rainforth, Robert Cornish, Hongseok Yang et al.

Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves involve calculation of a separate, nested, estimation. We investigate the statistical implications of nesting MC estimators, including cases of multiple levels of nesting, and establish the conditions under which they converge. We derive corresponding rates of convergence and provide empirical evidence that these rates are observed in practice. We further establish a number of pitfalls that can arise from naive nesting of MC estimators, provide guidelines about how these can be avoided, and lay out novel methods for reformulating certain classes of nested expectation problems into single expectations, leading to improved convergence rates. We demonstrate the applicability of our work by using our results to develop a new estimator for discrete Bayesian experimental design problems and derive error bounds for a class of variational objectives.