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Anqi Wu

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22 papers

2 author rows

ICML Conference 2025 Conference Paper

Inverse Reinforcement Learning with Switching Rewards and History Dependency for Characterizing Animal Behaviors

Jingyang Ke
Feiyang Wu
Jiyi Wang
Jeffrey Markowitz
Anqi Wu

Traditional approaches to studying decision-making in neuroscience focus on simplified behavioral tasks where animals perform repetitive, stereotyped actions to receive explicit rewards. While informative, these methods constrain our understanding of decision-making to short timescale behaviors driven by explicit goals. In natural environments, animals exhibit more complex, long-term behaviors driven by intrinsic motivations that are often unobservable. Recent works in time-varying inverse reinforcement learning (IRL) aim to capture shifting motivations in long-term, freely moving behaviors. However, a crucial challenge remains: animals make decisions based on their history, not just their current state. To address this, we introduce SWIRL (SWitching IRL), a novel framework that extends traditional IRL by incorporating time-varying, history-dependent reward functions. SWIRL models long behavioral sequences as transitions between short-term decision-making processes, each governed by a unique reward function. SWIRL incorporates biologically plausible history dependency to capture how past decisions and environmental contexts shape behavior, offering a more accurate description of animal decision-making. We apply SWIRL to simulated and real-world animal behavior datasets and show that it outperforms models lacking history dependency, both quantitatively and qualitatively. This work presents the first IRL model to incorporate history-dependent policies and rewards to advance our understanding of complex, naturalistic decision-making in animals.

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ICML Conference 2025 Conference Paper

Learning Time-Varying Multi-Region Brain Communications via Scalable Markovian Gaussian Processes

Weihan Li
Yule Wang
Chengrui Li
Anqi Wu

Understanding and constructing brain communications that capture dynamic communications across multiple regions is fundamental to modern system neuroscience, yet current methods struggle to find time-varying region-level communications or scale to large neural datasets with long recording durations. We present a novel framework using Markovian Gaussian Processes to learn brain communications with time-varying temporal delays from multi-region neural recordings, named Adaptive Delay Model (ADM). Our method combines Gaussian Processes with State Space Models and employs parallel scan inference algorithms, enabling efficient scaling to large datasets while identifying concurrent communication patterns that evolve over time. This time-varying approach captures how brain region interactions shift dynamically during cognitive processes. Validated on synthetic and multi-region neural recordings datasets, our approach discovers both the directionality and temporal dynamics of neural communication. This work advances our understanding of distributed neural computation and provides a scalable tool for analyzing dynamic brain networks.

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IJCAI Conference 2025 Conference Paper

Towards Fairness with Limited Demographics via Disentangled Learning

Zichong Wang
Anqi Wu
Nuno Moniz
Shu Hu
Bart Knijnenburg
Xingquan Zhu
Wenbin Zhang

Fairness in artificial intelligence has garnered increasing attention due to concerns about discriminatory AI-based decision-making, prompting the development of numerous mitigation approaches. However, most existing methods assume that demographic information is readily available, which may not align with real-world scenarios where such information is often incomplete. To this end, this paper tackles the pervasive yet overlooked challenge of developing fair machine learning algorithms with limited demographics. Specifically, we explore leveraging limited demographic information to accurately infer missing demographics while simultaneously evaluating and optimizing model fairness. We argue that this approach better aligns with common real-world socially sensitive scenarios involving limited demographics. Extensive experiments on three benchmark datasets highlight the effectiveness of the proposed method, surpassing state-of-the-art with significant gains in fairness while maintaining comparable utility.

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ICML Conference 2024 Conference Paper

A Differentiable Partially Observable Generalized Linear Model with Forward-Backward Message Passing

Chengrui Li
Weihan Li
Yule Wang
Anqi Wu

The partially observable generalized linear model (POGLM) is a powerful tool for understanding neural connectivities under the assumption of existing hidden neurons. With spike trains only recorded from visible neurons, existing works use variational inference to learn POGLM meanwhile presenting the difficulty of learning this latent variable model. There are two main issues: (1) the sampled Poisson hidden spike count hinders the use of the pathwise gradient estimator in VI; and (2) the existing design of the variational model is neither expressive nor time-efficient, which further affects the performance. For (1), we propose a new differentiable POGLM, which enables the pathwise gradient estimator, better than the score function gradient estimator used in existing works. For (2), we propose the forward-backward message-passing sampling scheme for the variational model. Comprehensive experiments show that our differentiable POGLMs with our forward-backward message passing produce a better performance on one synthetic and two real-world datasets. Furthermore, our new method yields more interpretable parameters, underscoring its significance in neuroscience.

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NeurIPS Conference 2024 Conference Paper

Exploring Behavior-Relevant and Disentangled Neural Dynamics with Generative Diffusion Models

Yule Wang
Chengrui Li
Weihan Li
Anqi Wu

Understanding the neural basis of behavior is a fundamental goal in neuroscience. Current research in large-scale neuro-behavioral data analysis often relies on decoding models, which quantify behavioral information in neural data but lack details on behavior encoding. This raises an intriguing scientific question: "how can we enable in-depth exploration of neural representations in behavioral tasks, revealing interpretable neural dynamics associated with behaviors". However, addressing this issue is challenging due to the varied behavioral encoding across different brain regions and mixed selectivity at the population level. To tackle this limitation, our approach, named ("BeNeDiff"), first identifies a fine-grained and disentangled neural subspace using a behavior-informed latent variable model. It then employs state-of-the-art generative diffusion models to synthesize behavior videos that interpret the neural dynamics of each latent factor. We validate the method on multi-session datasets containing widefield calcium imaging recordings across the dorsal cortex. Through guiding the diffusion model to activate individual latent factors, we verify that the neural dynamics of latent factors in the disentangled neural subspace provide interpretable quantifications of the behaviors of interest. At the same time, the neural subspace in BeNeDiff demonstrates high disentanglement and neural reconstruction quality.

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ICLR Conference 2024 Conference Paper

Forward χ2 Divergence Based Variational Importance Sampling

Chengrui Li
Yule Wang
Weihan Li
Anqi Wu

Maximizing the marginal log-likelihood is a crucial aspect of learning latent variable models, and variational inference (VI) stands as the commonly adopted method. However, VI can encounter challenges in achieving a high marginal log-likelihood when dealing with complicated posterior distributions. In response to this limitation, we introduce a novel variational importance sampling (VIS) approach that directly estimates and maximizes the marginal log-likelihood. VIS leverages the optimal proposal distribution, achieved by minimizing the forward $\chi^2$ divergence, to enhance marginal log-likelihood estimation. We apply VIS to various popular latent variable models, including mixture models, variational auto-encoders, and partially observable generalized linear models. Results demonstrate that our approach consistently outperforms state-of-the-art baselines, in terms of both log-likelihood and model parameter estimation. Code: \url{https://github.com/JerrySoybean/vis}.

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ICRA Conference 2024 Conference Paper

Infer and Adapt: Bipedal Locomotion Reward Learning from Demonstrations via Inverse Reinforcement Learning

Feiyang Wu
Zhaoyuan Gu
Hanran Wu
Anqi Wu
Ye Zhao 0002

Enabling bipedal walking robots to learn how to maneuver over highly uneven, dynamically changing terrains is challenging due to the complexity of robot dynamics and interacted environments. Recent advancements in learning from demonstrations have shown promising results for robot learning in complex environments. While imitation learning of expert policies has been well-explored, the study of learning expert reward functions is largely under-explored in legged locomotion. This paper brings state-of-the-art Inverse Reinforcement Learning (IRL) techniques to solving bipedal locomotion problems over complex terrains. We propose algorithms for learning expert reward functions, and we subsequently analyze the learned functions. Through nonlinear function approximation, we uncover meaningful insights into the expert’s locomotion strategies. Furthermore, we empirically demonstrate that training a bipedal locomotion policy with the inferred reward functions enhances its walking performance on unseen terrains, highlighting the adaptability offered by reward learning.

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TMLR Journal 2024 Journal Article

Inverse Kernel Decomposition

Chengrui Li
Anqi Wu

The state-of-the-art dimensionality reduction approaches largely rely on complicated optimization procedures. On the other hand, closed-form approaches requiring merely eigen-decomposition do not have enough sophistication and nonlinearity. In this paper, we propose a novel nonlinear dimensionality reduction method---Inverse Kernel Decomposition (IKD)---based on an eigen-decomposition of the sample covariance matrix of data. The method is inspired by Gaussian process latent variable models (GPLVMs) and has comparable performance with GPLVMs. To deal with very noisy data with weak correlations, we propose two solutions---blockwise and geodesic---to make use of locally correlated data points and provide better and numerically more stable latent estimations. We use synthetic datasets and four real-world datasets to show that IKD is a better dimensionality reduction method than other eigen-decomposition-based methods, and achieves comparable performance against optimization-based methods with faster running speeds. Open-source IKD implementation in Python can be accessed at \url{https://github.com/JerrySoybean/ikd}.

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ICML Conference 2024 Conference Paper

Multi-Region Markovian Gaussian Process: An Efficient Method to Discover Directional Communications Across Multiple Brain Regions

Weihan Li
Chengrui Li
Yule Wang
Anqi Wu

Studying the complex interactions between different brain regions is crucial in neuroscience. Various statistical methods have explored the latent communication across multiple brain regions. Two main categories are the Gaussian Process (GP) and Linear Dynamical System (LDS), each with unique strengths. The GP-based approach effectively discovers latent variables with frequency bands and communication directions. Conversely, the LDS-based approach is computationally efficient but lacks powerful expressiveness in latent representation. In this study, we merge both methodologies by creating an LDS mirroring a multi-output GP, termed Multi-Region Markovian Gaussian Process (MRM-GP). Our work establishes a connection between an LDS and a multi-output GP that explicitly models frequencies and phase delays within the latent space of neural recordings. Consequently, the model achieves a linear inference cost over time points and provides an interpretable low-dimensional representation, revealing communication directions across brain regions and separating oscillatory communications into different frequency bands.

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ICLR Conference 2024 Conference Paper

One-hot Generalized Linear Model for Switching Brain State Discovery

Chengrui Li
Soon Ho Kim
Chris Rodgers
Hannah Choi
Anqi Wu

Exposing meaningful and interpretable neural interactions is critical to understanding neural circuits. Inferred neural interactions from neural signals primarily reflect functional connectivity. In a long experiment, subject animals may experience different stages defined by the experiment, stimuli, or behavioral states, and hence functional connectivity can change over time. To model dynamically changing functional connectivity, prior work employs state-switching generalized linear models with hidden Markov models (i.e., HMM-GLMs). However, we argue they lack biological plausibility, as functional connectivities are shaped and confined by the underlying anatomical connectome. Here, we propose two novel prior-informed state-switching GLMs, called Gaussian HMM-GLM (Gaussian prior) and one-hot HMM-GLM (Gumbel-Softmax one-hot prior). We show that the learned prior should capture the state-invariant interaction, shedding light on the underlying anatomical connectome and revealing more likely physical neuron interactions. The state-dependent interaction modeled by each GLM offers traceability to capture functional variations across multiple brain states. Our methods effectively recover true interaction structures in simulated data, achieve the highest predictive likelihood, and enhance the interpretability of interaction patterns and hidden states when applied to real neural data. The code is available at \url{https://github.com/JerrySoybean/onehot-hmmglm}.

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NeurIPS Conference 2023 Conference Paper

Extraction and Recovery of Spatio-Temporal Structure in Latent Dynamics Alignment with Diffusion Models

Yule Wang
Zijing Wu
Chengrui Li
Anqi Wu

In the field of behavior-related brain computation, it is necessary to align raw neural signals against the drastic domain shift among them. A foundational framework within neuroscience research posits that trial-based neural population activities rely on low-dimensional latent dynamics, thus focusing on the latter greatly facilitates the alignment procedure. Despite this field's progress, existing methods ignore the intrinsic spatio-temporal structure during the alignment phase. Hence, their solutions usually lead to poor quality in latent dynamics structures and overall performance. To tackle this problem, we propose an alignment method ERDiff, which leverages the expressivity of the diffusion model to preserve the spatio-temporal structure of latent dynamics. Specifically, the latent dynamics structures of the source domain are first extracted by a diffusion model. Then, under the guidance of this diffusion model, such structures are well-recovered through a maximum likelihood alignment procedure in the target domain. We first demonstrate the effectiveness of our proposed method on a synthetic dataset. Then, when applied to neural recordings from the non-human primate motor cortex, under both cross-day and inter-subject settings, our method consistently manifests its capability of preserving the spatio-temporal structure of latent dynamics and outperforms existing approaches in alignment goodness-of-fit and neural decoding performance.

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NeurIPS Conference 2023 Conference Paper

Inverse Reinforcement Learning with the Average Reward Criterion

Feiyang Wu
Jingyang Ke
Anqi Wu

We study the problem of Inverse Reinforcement Learning (IRL) with an average-reward criterion. The goal is to recover an unknown policy and a reward function when the agent only has samples of states and actions from an experienced agent. Previous IRL methods assume that the expert is trained in a discounted environment, and the discount factor is known. This work alleviates this assumption by proposing an average-reward framework with efficient learning algorithms. We develop novel stochastic first-order methods to solve the IRL problem under the average-reward setting, which requires solving an Average-reward Markov Decision Process (AMDP) as a subproblem. To solve the subproblem, we develop a Stochastic Policy Mirror Descent (SPMD) method under general state and action spaces that needs $\mathcal{O}(1/\varepsilon)$ steps of gradient computation. Equipped with SPMD, we propose the Inverse Policy Mirror Descent (IPMD) method for solving the IRL problem with a $\mathcal{O}(1/\varepsilon^2)$ complexity. To the best of our knowledge, the aforementioned complexity results are new in IRL with the average reward criterion. Finally, we corroborate our analysis with numerical experiments using the MuJoCo benchmark and additional control tasks.

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YNIMG Journal 2021 Journal Article

Brain kernel: A new spatial covariance function for fMRI data

Anqi Wu
Samuel A. Nastase
Christopher A. Baldassano
Nicholas B. Turk-Browne
Kenneth A. Norman
Barbara E. Engelhardt
Jonathan W. Pillow

A key problem in functional magnetic resonance imaging (fMRI) is to estimate spatial activity patterns from noisy high-dimensional signals. Spatial smoothing provides one approach to regularizing such estimates. However, standard smoothing methods ignore the fact that correlations in neural activity may fall off at different rates in different brain areas, or exhibit discontinuities across anatomical or functional boundaries. Moreover, such methods do not exploit the fact that widely separated brain regions may exhibit strong correlations due to bilateral symmetry or the network organization of brain regions. To capture this non-stationary spatial correlation structure, we introduce the brain kernel, a continuous covariance function for whole-brain activity patterns. We define the brain kernel in terms of a continuous nonlinear mapping from 3D brain coordinates to a latent embedding space, parametrized with a Gaussian process (GP). The brain kernel specifies the prior covariance between voxels as a function of the distance between their locations in embedding space. The GP mapping warps the brain nonlinearly so that highly correlated voxels are close together in latent space, and uncorrelated voxels are far apart. We estimate the brain kernel using resting-state fMRI data, and we develop an exact, scalable inference method based on block coordinate descent to overcome the challenges of high dimensionality (10-100K voxels). Finally, we illustrate the brain kernel's usefulness with applications to brain decoding and factor analysis with multiple task-based fMRI datasets.

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NeurIPS Conference 2021 Conference Paper

Neural Latents Benchmark ‘21: Evaluating latent variable models of neural population activity

Felix Pei
Joel Ye
David Zoltowski
Anqi Wu
Raeed Chowdhury
Hansem Sohn
Joseph O'Doherty
Krishna V Shenoy

Advances in neural recording present increasing opportunities to study neural activity in unprecedented detail. Latent variable models (LVMs) are promising tools for analyzing this rich activity across diverse neural systems and behaviors, as LVMs do not depend on known relationships between the activity and external experimental variables. However, progress with LVMs for neuronal population activity is currently impeded by a lack of standardization, resulting in methods being developed and compared in an ad hoc manner. To coordinate these modeling efforts, we introduce a benchmark suite for latent variable modeling of neural population activity. We curate four datasets of neural spiking activity from cognitive, sensory, and motor areas to promote models that apply to the wide variety of activity seen across these areas. We identify unsupervised evaluation as a common framework for evaluating models across datasets, and apply several baselines that demonstrate the variety of the benchmarked datasets. We release this benchmark through EvalAI. http: //neurallatents. github. io

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NeurIPS Conference 2020 Conference Paper

Deep Graph Pose: a semi-supervised deep graphical model for improved animal pose tracking

Anqi Wu
Estefany Kelly Buchanan
Matthew Whiteway
Michael Schartner
Guido Meijer
Jean-Paul Noel
Erica Rodriguez
Claire Everett

Noninvasive behavioral tracking of animals is crucial for many scientific investigations. Recent transfer learning approaches for behavioral tracking have considerably advanced the state of the art. Typically these methods treat each video frame and each object to be tracked independently. In this work, we improve on these methods (particularly in the regime of few training labels) by leveraging the rich spatiotemporal structures pervasive in behavioral video --- specifically, the spatial statistics imposed by physical constraints (e. g. , paw to elbow distance), and the temporal statistics imposed by smoothness from frame to frame. We propose a probabilistic graphical model built on top of deep neural networks, Deep Graph Pose (DGP), to leverage these useful spatial and temporal constraints, and develop an efficient structured variational approach to perform inference in this model. The resulting semi-supervised model exploits both labeled and unlabeled frames to achieve significantly more accurate and robust tracking while requiring users to label fewer training frames. In turn, these tracking improvements enhance performance on downstream applications, including robust unsupervised segmentation of behavioral syllables, '' and estimation of interpretable disentangled'' low-dimensional representations of the full behavioral video. Open source code is available at \href{\CodeLink}{https: //github. com/paninski-lab/deepgraphpose}.

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JMLR Journal 2019 Journal Article

Dependent relevance determination for smooth and structured sparse regression

Anqi Wu
Oluwasanmi Koyejo
Jonathan Pillow

In many problem settings, parameter vectors are not merely sparse but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as “region sparsity.” Classical sparse regression methods, such as the lasso and automatic relevance determination (ARD), which model parameters as independent a priori, and therefore do not exploit such dependencies. Here we introduce a hierarchical model for smooth, region-sparse weight vectors and tensors in a linear regression setting. Our approach represents a hierarchical extension of the relevance determination framework, where we add a transformed Gaussian process to model the dependencies between the prior variances of regression weights. We combine this with a structured model of the prior variances of Fourier coefficients, which eliminates unnecessary high frequencies. The resulting prior encourages weights to be region-sparse in two different bases simultaneously. We develop Laplace approximation and Monte Carlo Markov Chain (MCMC) sampling to provide efficient inference for the posterior. Furthermore, a two-stage convex relaxation of the Laplace approximation approach is also provided to relax the inevitable non-convexity during the optimization. We finally show substantial improvements over comparable methods for both simulated and real datasets from brain imaging. [abs] [ pdf ][ bib ] &copy JMLR 2019. ( edit, beta )

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ICLR Conference 2019 Conference Paper

Deterministic Variational Inference for Robust Bayesian Neural Networks

Anqi Wu
Sebastian Nowozin
Edward Meeds
Richard E. Turner
José Miguel Hernández-Lobato
Alex Gaunt

Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes (VB) is theoretically grounded, generally applicable, and computationally efficient. With wide recognition of potential advantages, why is it that variational Bayes has seen very limited practical use for BNNs in real applications? We argue that variational inference in neural networks is fragile: successful implementations require careful initialization and tuning of prior variances, as well as controlling the variance of Monte Carlo gradient estimates. We provide two innovations that aim to turn VB into a robust inference tool for Bayesian neural networks: first, we introduce a novel deterministic method to approximate moments in neural networks, eliminating gradient variance; second, we introduce a hierarchical prior for parameters and a novel Empirical Bayes procedure for automatically selecting prior variances. Combining these two innovations, the resulting method is highly efficient and robust. On the application of heteroscedastic regression we demonstrate good predictive performance over alternative approaches.

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UAI Conference 2019 Conference Paper

Neural Dynamics Discovery via Gaussian Process Recurrent Neural Networks

Qi She
Anqi Wu

Latent dynamics discovery is challenging in extracting complex dynamics from highdimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent trajectories. However, simple state transition structures, linear embedding assumptions, or inflexible inference networks impede the accurate recovery of dynamic portraits. In this paper, we propose a novel latent dynamic model that is capable of capturing nonlinear, non- Markovian, long short-term time-dependent dynamics via recurrent neural networks and tackling complex nonlinear embedding via non-parametric Gaussian process. Due to the complexity and intractability of the model and its inference, we also provide a powerful inference network with bi-directional long short-term memory networks that encode both past and future information into posterior distributions. In the experiment, we show that our model outperforms other state-of-the-art methods in reconstructing insightful latent dynamics from both simulated and experimental neural datasets with either Gaussian or Poisson observations, especially in the low-sample scenario. Our codes and additional materials are available at https: //github. com/sheqi/GP-RNN_UAI2019.

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NeurIPS Conference 2018 Conference Paper

Learning a latent manifold of odor representations from neural responses in piriform cortex

Anqi Wu
Stan Pashkovski
Sandeep Datta
Jonathan Pillow

A major difficulty in studying the neural mechanisms underlying olfactory perception is the lack of obvious structure in the relationship between odorants and the neural activity patterns they elicit. Here we use odor-evoked responses in piriform cortex to identify a latent manifold specifying latent distance relationships between olfactory stimuli. Our approach is based on the Gaussian process latent variable model, and seeks to map odorants to points in a low-dimensional embedding space, where distances between points in the embedding space relate to the similarity of population responses they elicit. The model is specified by an explicit continuous mapping from a latent embedding space to the space of high-dimensional neural population firing rates via nonlinear tuning curves, each parametrized by a Gaussian process. Population responses are then generated by the addition of correlated, odor-dependent Gaussian noise. We fit this model to large-scale calcium fluorescence imaging measurements of population activity in layers 2 and 3 of mouse piriform cortex following the presentation of a diverse set of odorants. The model identifies a low-dimensional embedding of each odor, and a smooth tuning curve over the latent embedding space that accurately captures each neuron's response to different odorants. The model captures both signal and noise correlations across more than 500 neurons. We validate the model using a cross-validation analysis known as co-smoothing to show that the model can accurately predict the responses of a population of held-out neurons to test odorants.

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NeurIPS Conference 2017 Conference Paper

Gaussian process based nonlinear latent structure discovery in multivariate spike train data

Anqi Wu
Nicholas Roy
Stephen Keeley
Jonathan Pillow

A large body of recent work focuses on methods for extracting low-dimensional latent structure from multi-neuron spike train data. Most such methods employ either linear latent dynamics or linear mappings from latent space to log spike rates. Here we propose a doubly nonlinear latent variable model that can identify low-dimensional structure underlying apparently high-dimensional spike train data. We introduce the Poisson Gaussian-Process Latent Variable Model (P-GPLVM), which consists of Poisson spiking observations and two underlying Gaussian processes—one governing a temporal latent variable and another governing a set of nonlinear tuning curves. The use of nonlinear tuning curves enables discovery of low-dimensional latent structure even when spike responses exhibit high linear dimensionality (e. g. , as found in hippocampal place cell codes). To learn the model from data, we introduce the decoupled Laplace approximation, a fast approximate inference method that allows us to efficiently optimize the latent path while marginalizing over tuning curves. We show that this method outperforms previous Laplace-approximation-based inference methods in both the speed of convergence and accuracy. We apply the model to spike trains recorded from hippocampal place cells and show that it compares favorably to a variety of previous methods for latent structure discovery, including variational auto-encoder (VAE) based methods that parametrize the nonlinear mapping from latent space to spike rates with a deep neural network.

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NeurIPS Conference 2015 Conference Paper

Convolutional spike-triggered covariance analysis for neural subunit models

Anqi Wu
Il Memming Park
Jonathan Pillow

Subunit models provide a powerful yet parsimonious description of neural spike responses to complex stimuli. They can be expressed by a cascade of two linear-nonlinear (LN) stages, with the first linear stage defined by convolution with one or more filters. Recent interest in such models has surged due to their biological plausibility and accuracy for characterizing early sensory responses. However, fitting subunit models poses a difficult computational challenge due to the expense of evaluating the log-likelihood and the ubiquity of local optima. Here we address this problem by forging a theoretical connection between spike-triggered covariance analysis and nonlinear subunit models. Specifically, we show that a ''convolutional'' decomposition of the spike-triggered average (STA) and covariance (STC) provides an asymptotically efficient estimator for the subunit model under certain technical conditions. We also prove the identifiability of such convolutional decomposition under mild assumptions. Our moment-based methods outperform highly regularized versions of the GQM on neural data from macaque primary visual cortex, and achieves nearly the same prediction performance as the full maximum-likelihood estimator, yet with substantially lower cost.

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NeurIPS Conference 2014 Conference Paper

Sparse Bayesian structure learning with “dependent relevance determination” priors

Anqi Wu
Mijung Park
Oluwasanmi Koyejo
Jonathan Pillow

In many problem settings, parameter vectors are not merely sparse, but dependent in such a way that non-zero coefficients tend to cluster together. We refer to this form of dependency as “region sparsity”. Classical sparse regression methods, such as the lasso and automatic relevance determination (ARD), model parameters as independent a priori, and therefore do not exploit such dependencies. Here we introduce a hierarchical model for smooth, region-sparse weight vectors and tensors in a linear regression setting. Our approach represents a hierarchical extension of the relevance determination framework, where we add a transformed Gaussian process to model the dependencies between the prior variances of regression weights. We combine this with a structured model of the prior variances of Fourier coefficients, which eliminates unnecessary high frequencies. The resulting prior encourages weights to be region-sparse in two different bases simultaneously. We develop efficient approximate inference methods and show substantial improvements over comparable methods (e. g. , group lasso and smooth RVM) for both simulated and real datasets from brain imaging.

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