Emily B. Fox

UAI Conference 2025 Conference Paper

HDP-Flow: Generalizable Bayesian Nonparametric Model for Time Series State Discovery

• Sana Tonekaboni
• Tina Behrouzi
• Addison Weatherhead
• Emily B. Fox
• David M. Blei
• Anna Goldenberg

We introduce HDP-Flow, a Bayesian nonparametric (BNP) model for unsupervised state discovery in dynamic, non-stationary time series data. Unlike prior work that assumes fixed states, HDPFlow models evolving datasets with unknown and variable latent states. By integrating the adaptability of BNP models with the expressive power of normalizing flows, HDP-Flow effectively models dynamic, non-stationary patterns, while learning transferable states across datasets with wellcalibrated uncertainty. We propose a scalable variational algorithm to enable efficient inference, addressing the limitations of traditional sampling-based BNP methods. HDP-Flow outperforms existing approaches in latent state identification and provides probabilistic insight into state distributions and transition dynamics. Evaluating HDP-Flow across two wearable datasets demonstrates transferability of states across diverse sub-populations, validating its robustness and generalizability.

ICML Conference 2024 Conference Paper

Automated Statistical Model Discovery with Language Models

• Michael Y. Li
• Emily B. Fox
• Noah D. Goodman

Statistical model discovery is a challenging search over a vast space of models subject to domain-specific constraints. Efficiently searching over this space requires expertise in modeling and the problem domain. Motivated by the domain knowledge and programming capabilities of large language models (LMs), we introduce a method for language model driven automated statistical model discovery. We cast our automated procedure within the principled framework of Box’s Loop: the LM iterates between proposing statistical models represented as probabilistic programs, acting as a modeler, and critiquing those models, acting as a domain expert. By leveraging LMs, we do not have to define a domain-specific language of models or design a handcrafted search procedure, which are key restrictions of previous systems. We evaluate our method in three settings in probabilistic modeling: searching within a restricted space of models, searching over an open-ended space, and improving expert models under natural language constraints (e. g. , this model should be interpretable to an ecologist). Our method identifies models on par with human expert designed models and extends classic models in interpretable ways. Our results highlight the promise of LM-driven model discovery.

ICML Conference 2024 Conference Paper

Hybrid2 Neural ODE Causal Modeling and an Application to Glycemic Response

• Bob Junyi Zou
• Matthew E. Levine
• Dessi P. Zaharieva
• Ramesh Johari
• Emily B. Fox

Hybrid models composing mechanistic ODE-based dynamics with flexible and expressive neural network components have grown rapidly in popularity, especially in scientific domains where such ODE-based modeling offers important interpretability and validated causal grounding (e. g. , for counterfactual reasoning). The incorporation of mechanistic models also provides inductive bias in standard blackbox modeling approaches, critical when learning from small datasets or partially observed, complex systems. Unfortunately, as the hybrid models become more flexible, the causal grounding provided by the mechanistic model can quickly be lost. We address this problem by leveraging another common source of domain knowledge: ranking of treatment effects for a set of interventions, even if the precise treatment effect is unknown. We encode this information in a causal loss that we combine with the standard predictive loss to arrive at a hybrid loss that biases our learning towards causally valid hybrid models. We demonstrate our ability to achieve a win-win, state-of-the-art predictive performance and causal validity, in the challenging task of modeling glucose dynamics post-exercise in individuals with type 1 diabetes.

ICML Conference 2023 Conference Paper

Sequence Modeling with Multiresolution Convolutional Memory

• Jiaxin Shi
• Ke Alexander Wang
• Emily B. Fox

Efficiently capturing the long-range patterns in sequential data sources salient to a given task—such as classification and generative modeling—poses a fundamental challenge. Popular approaches in the space tradeoff between the memory burden of brute-force enumeration and comparison, as in transformers, the computational burden of complicated sequential dependencies, as in recurrent neural networks, or the parameter burden of convolutional networks with many or large filters. We instead take inspiration from wavelet-based multiresolution analysis to define a new building block for sequence modeling, which we call a MultiresLayer. The key component of our model is the multiresolution convolution, capturing multiscale trends in the input sequence. Our MultiresConv can be implemented with shared filters across a dilated causal convolution tree. Thus it garners the computational advantages of convolutional networks and the principled theoretical motivation of wavelet decompositions. Our MultiresLayer is straightforward to implement, requires significantly fewer parameters, and maintains at most a $O(N \log N)$ memory footprint for a length $N$ sequence. Yet, by stacking such layers, our model yields state-of-the-art performance on a number of sequence classification and autoregressive density estimation tasks using CIFAR-10, ListOps, and PTB-XL datasets.

ICRA Conference 2019 Conference Paper

A Simple Adaptive Tracker with Reminiscences

• Christopher Xie
• Emily B. Fox
• Zaïd Harchaoui

Correlation filters have provided exceptional results in the field of visual object tracking in the past few years. However, these methods typically learn a single filter to be robust to many different appearance changes, which can be challenging. We propose a simple solution to this problem by utilizing an ensemble method of base trackers trained on different temporal windows of the video history. The proposed tracker, called MTCF, exhibits the following features: i) it can be trained using gradient-based convex optimization; ii) it is robust to short-term and long-term changes in visual appearance. MTCF performs on par with or outperforms state-of-the-art trackers on the OTB and the VOT benchmark datasets. We present an extensive analysis of the performance of MTCF on these benchmark datasets.

UAI Conference 2019 Conference Paper

Adaptively Truncating Backpropagation Through Time to Control Gradient Bias

• Christopher Aicher
• Nicholas J. Foti
• Emily B. Fox

Truncated backpropagation through time (TBPTT) is a popular method for learning in recurrent neural networks (RNNs) that saves computation and memory at the cost of bias by truncating backpropagation after a fixed number of lags. In practice, choosing the optimal truncation length is difficult: TBPTT will not converge if the truncation length is too small, or will converge slowly if it is too large. We propose an adaptive TBPTT scheme that converts the problem from choosing a temporal lag to one of choosing a tolerable amount of gradient bias. For many realistic RNNs, the TBPTT gradients decay geometrically in expectation for large lags; under this condition, we can control the bias by varying the truncation length adaptively. For RNNs with smooth activation functions, we prove that this bias controls the convergence rate of SGD with biased gradients for our non-convex loss. Using this theory, we develop a practical method for adaptively estimating the truncation length during training. We evaluate our adaptive TBPTT method on synthetic data and language modeling tasks and find that our adaptive TBPTT ameliorates the computational pitfalls of fixed TBPTT.

ICML Conference 2018 Conference Paper

oi-VAE: Output Interpretable VAEs for Nonlinear Group Factor Analysis

• Samuel K. Ainsworth
• Nicholas J. Foti
• Adrian K. C. Lee
• Emily B. Fox

Deep generative models have recently yielded encouraging results in producing subjectively realistic samples of complex data. Far less attention has been paid to making these generative models interpretable. In many scenarios, ranging from scientific applications to finance, the observed variables have a natural grouping. It is often of interest to understand systems of interaction amongst these groups, and latent factor models (LFMs) are an attractive approach. However, traditional LFMs are limited by assuming a linear correlation structure. We present an output interpretable VAE (oi-VAE) for grouped data that models complex, nonlinear latent-to-observed relationships. We combine a structured VAE comprised of group-specific generators with a sparsity-inducing prior. We demonstrate that oi-VAE yields meaningful notions of interpretability in the analysis of motion capture and MEG data. We further show that in these situations, the regularization inherent to oi-VAE can actually lead to improved generalization and learned generative processes.

ICML Conference 2017 Conference Paper

Stochastic Gradient MCMC Methods for Hidden Markov Models

• Yian Ma
• Nicholas J. Foti
• Emily B. Fox

Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i. i. d data. We instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov models (HMMs) for time-dependent data. There are two challenges to applying SG-MCMC in this setting: The latent discrete states, and needing to break dependencies when considering minibatches. We consider a marginal likelihood representation of the HMM and propose an algorithm that harnesses the inherent memory decay of the process. We demonstrate the effectiveness of our algorithm on synthetic experiments and an ion channel recording data, with runtimes significantly outperforming batch MCMC.

JMLR Journal 2015 Journal Article

Bayesian Nonparametric Covariance Regression

• Emily B. Fox
• David B. Dunson

Capturing predictor-dependent correlations amongst the elements of a multivariate response vector is fundamental to numerous applied domains, including neuroscience, epidemiology, and finance. Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, relatively little has been done in the multivariate case. As a motivating example, we consider the Google Flu Trends data set, which provides indirect measurements of influenza incidence at a large set of locations over time (our predictor). To accurately characterize temporally evolving influenza incidence across regions, it is important to develop statistical methods for a time-varying covariance matrix. Importantly, the locations provide a redundant set of measurements and do not yield a sparse nor static spatial dependence structure. We propose to reduce dimensionality and induce a flexible Bayesian nonparametric covariance regression model by relating these location-specific trajectories to a lower-dimensional subspace through a latent factor model with predictor-dependent factor loadings. These loadings are in terms of a collection of basis functions that vary nonparametrically over the predictor space. Such low-rank approximations are in contrast to sparse precision assumptions, and are appropriate in a wide range of applications. Our formulation aims to address three challenges: scaling to large $p$ domains, coping with missing values, and allowing an irregular grid of observations. The model is shown to be highly flexible, while leading to a computationally feasible implementation via Gibbs sampling. The ability to scale to large $p$ domains and cope with missing values is fundamental in analyzing the Google Flu Trends data. [abs] [ pdf ][ bib ] &copy JMLR 2015. ( edit, beta )

UAI Conference 2015 Conference Paper

Bayesian Structure Learning for Stationary Time Series

• Alex Tank
• Nicholas J. Foti
• Emily B. Fox

While much work has explored probabilistic graphical models for independent data, less attention has been paid to time series. The goal in this setting is to determine conditional independence relations between entire time series, which for stationary series, are encoded by zeros in the inverse spectral density matrix. We take a Bayesian approach to structure learning, placing priors on (i) the graph structure and (ii) spectral matrices given the graph. We leverage a Whittle likelihood approximation and define a conjugate prior—the hyper complex inverse Wishart—on the complex-valued and graph-constrained spectral matrices. Due to conjugacy, we can analytically marginalize the spectral matrices and obtain a closed-form marginal likelihood of the time series given a graph. Importantly, our analytic marginal likelihood allows us to avoid inference of the complex spectral matrices themselves and places us back into the framework of standard (Bayesian) structure learning. In particular, combining this marginal likelihood with our graph prior leads to efficient inference of the time series graph itself, which we base on a stochastic search procedure, though any standard approach can be straightforwardly modified to our time series case. We demonstrate our methods on analyzing stock data and neuroimaging data of brain activity during various auditory tasks.

ICML Conference 2014 Conference Paper

Learning the Parameters of Determinantal Point Process Kernels

• Raja Hafiz Affandi
• Emily B. Fox
• Ryan P. Adams
• Ben Taskar

Determinantal point processes (DPPs) are well-suited for modeling repulsion and have proven useful in applications where diversity is desired. While DPPs have many appealing properties, learning the parameters of a DPP is difficult, as the likelihood is non-convex and is infeasible to compute in many scenarios. Here we propose Bayesian methods for learning the DPP kernel parameters. These methods are applicable in large-scale discrete and continuous DPP settings, even when the likelihood can only be bounded. We demonstrate the utility of our DPP learning methods in studying the progression of diabetic neuropathy based on the spatial distribution of nerve fibers, and in studying human perception of diversity in images.

AIJ Journal 2014 Journal Article

Modeling the complex dynamics and changing correlations of epileptic events

• Drausin F. Wulsin
• Emily B. Fox
• Brian Litt

Patients with epilepsy can manifest short, sub-clinical epileptic “bursts” in addition to full-blown clinical seizures. We believe the relationship between these two classes of events—something not previously studied quantitatively—could yield important insights into the nature and intrinsic dynamics of seizures. A goal of our work is to parse these complex epileptic events into distinct dynamic regimes. A challenge posed by the intracranial EEG (iEEG) data we study is the fact that the number and placement of electrodes can vary between patients. We develop a Bayesian nonparametric Markov switching process that allows for (i) shared dynamic regimes between a variable number of channels, (ii) asynchronous regime-switching, and (iii) an unknown dictionary of dynamic regimes. We encode a sparse and changing set of dependencies between the channels using a Markov-switching Gaussian graphical model for the innovations process driving the channel dynamics and demonstrate the importance of this model in parsing and out-of-sample predictions of iEEG data. We show that our model produces intuitive state assignments that can help automate clinical analysis of seizures and enable the comparison of sub-clinical bursts and full clinical seizures.

ICML Conference 2014 Conference Paper

Stochastic Gradient Hamiltonian Monte Carlo

• Tianqi Chen 0001
• Emily B. Fox
• Carlos Guestrin

Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for defining distant proposals with high acceptance probabilities in a Metropolis-Hastings framework, enabling more efficient exploration of the state space than standard random-walk proposals. The popularity of such methods has grown significantly in recent years. However, a limitation of HMC methods is the required gradient computation for simulation of the Hamiltonian dynamical system-such computation is infeasible in problems involving a large sample size or streaming data. Instead, we must rely on a noisy gradient estimate computed from a subset of the data. In this paper, we explore the properties of such a stochastic gradient HMC approach. Surprisingly, the natural implementation of the stochastic approximation can be arbitrarily bad. To address this problem we introduce a variant that uses second-order Langevin dynamics with a friction term that counteracts the effects of the noisy gradient, maintaining the desired target distribution as the invariant distribution. Results on simulated data validate our theory. We also provide an application of our methods to a classification task using neural networks and to online Bayesian matrix factorization.

ICML Conference 2013 Conference Paper

Parsing epileptic events using a Markov switching process model for correlated time series

• Drausin Wulsin
• Emily B. Fox
• Brian Litt

Patients with epilepsy can manifest short, sub-clinical epileptic “bursts” in addition to full-blown clinical seizures. We believe the relationship between these two classes of events—something not previously studied quantitatively—could yield important insights into the nature and intrinsic dynamics of seizures. A goal of our work is to parse these complex epileptic events into distinct dynamic regimes. A challenge posed by the intracranial EEG (iEEG) data we study is the fact that the number and placement of electrodes can vary between patients. We develop a Bayesian nonparametric Markov switching process that allows for (i) shared dynamic regimes between a variable numbers of channels, (ii) asynchronous regime-switching, and (iii) an unknown dictionary of dynamic regimes. We encode a sparse and changing set of dependencies between the channels using a Markov-switching Gaussian graphical model for the innovations process driving the channel dynamics. We demonstrate the importance of this model in parsing and out-of-sample predictions of iEEG data. We show that our model produces intuitive state assignments that can help automate clinical analysis of seizures and enable the comparison of sub-clinical bursts and full clinical seizures.

UAI Conference 2012 Conference Paper

Markov Determinantal Point Processes

• Raja Hafiz Affandi
• Alex Kulesza
• Emily B. Fox

A determinantal point process (DPP) is a random process useful for modeling the combinatorial problem of subset selection. In particular, DPPs encourage a random subset Y to contain a diverse set of items selected from a base set Y. For example, we might use a DPP to display a set of news headlines that are relevant to a user’s interests while covering a variety of topics. Suppose, however, that we are asked to sequentially select multiple diverse sets of items, for example, displaying new headlines day-by-day. We might want these sets to be diverse not just individually but also through time, offering headlines today that are unlike the ones shown yesterday. In this paper, we construct a Markov DPP (M-DPP) that models a sequence of random sets {Y t}. The proposed M-DPP defines a stationary process that maintains DPP margins. Crucially, the induced union process Zt ≡ Y t∪Y t−1 is also marginally DPP-distributed. Jointly, these properties imply that the sequence of random sets are encouraged to be diverse both at a given time step as well as across time steps. We describe an exact, efficient sampling procedure, and a method for incrementally learning a quality measure over items in the base set Y based on external preferences. We apply the M-DPP to the task of sequentially displaying diverse and relevant news articles to a user with topic preferences.

ICML Conference 2008 Conference Paper

An HDP-HMM for systems with state persistence

• Emily B. Fox
• Erik B. Sudderth
• Michael I. Jordan
• Alan S. Willsky