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Greg Ver Steeg

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32 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Exploring the Design Space of Diffusion Bridge Models

Shaorong Zhang
Yuanbin Cheng
Greg Ver Steeg

Diffusion bridge models and stochastic interpolants enable high-quality image-to-image (I2I) translation by creating paths between distributions in pixel space. However, recent diffusion bridge models excel in image translation but suffer from restricted design flexibility and complicated hyperparameter tuning, whereas Stochastic Interpolants offer greater flexibility but lack essential refinements. We show that these complementary strengths can be unified by interpreting all existing methods within a single SI-based framework. In this work, we unify and expand the space of bridge models by extending Stochastic Interpolants (SIs) with preconditioning, endpoint conditioning, and an optimized sampling algorithm. These enhancements expand the design space of diffusion bridge models, leading to state-of-the-art performance in both image quality and sampling efficiency across diverse I2I tasks. Furthermore, we identify and address a previously overlooked issue of low sample diversity under fixed conditions. We introduce a quantitative analysis for output diversity and demonstrate how we can modify the base distribution for further improvements.

ICLR Conference 2024 Conference Paper

Interpretable Diffusion via Information Decomposition

Xianghao Kong
Ollie Liu
Han Li
Dani Yogatama
Greg Ver Steeg

Denoising diffusion models enable conditional generation and density modeling of complex relationships like images and text. However, the nature of the learned relationships is opaque making it difficult to understand precisely what relationships between words and parts of an image are captured, or to predict the effect of an intervention. We illuminate the fine-grained relationships learned by diffusion models by noticing a precise relationship between diffusion and information decomposition. Exact expressions for mutual information and conditional mutual information can be written in terms of the denoising model. Furthermore, ${pointwise}$ estimates can be easily estimated as well, allowing us to ask questions about the relationships between specific images and captions. Decomposing information even further to understand which variables in a high-dimensional space carry information is a long-standing problem. For diffusion models, we show that a natural non-negative decomposition of mutual information emerges, allowing us to quantify informative relationships between words and pixels in an image. We exploit these new relations to measure the compositional understanding of diffusion models, to do unsupervised localization of objects in images, and to measure effects when selectively editing images through prompt interventions.

ICLR Conference 2023 Conference Paper

Information-Theoretic Diffusion

Xianghao Kong
Rob Brekelmans
Greg Ver Steeg

Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models inspired by classic results in information theory that connect Information with Minimum Mean Square Error regression, the so-called I-MMSE relations. We generalize the I-MMSE relations to \emph{exactly} relate the data distribution to an optimal denoising regression problem, leading to an elegant refinement of existing diffusion bounds. This new insight leads to several improvements for probability distribution estimation, including a theoretical justification for diffusion model ensembling. Remarkably, our framework shows how continuous and discrete probabilities can be learned with the same regression objective, avoiding domain-specific generative models used in variational methods.

UAI Conference 2023 Conference Paper

Partial identification of dose responses with hidden confounders

Myrl G. Marmarelis
Elizabeth Haddad
Andrew Jesson
Neda Jahanshad
Aram Galstyan
Greg Ver Steeg

Inferring causal effects of continuous-valued treatments from observational data is a crucial task promising to better inform policy- and decision-makers. A critical assumption needed to identify these effects is that all confounding variables—causal parents of both the treatment and the outcome—are included as covariates. Unfortunately, given observational data alone, we cannot know with certainty that this criterion is satisfied. Sensitivity analyses provide principled ways to give bounds on causal estimates when confounding variables are hidden. While much attention is focused on sensitivity analyses for discrete-valued treatments, much less is paid to continuous-valued treatments. We present novel methodology to bound both average and conditional average continuous-valued treatment-effect estimates when they cannot be point identified due to hidden confounding. A semi-synthetic benchmark on multiple datasets shows our method giving tighter coverage of the true dose-response curve than a recently proposed continuous sensitivity model and baselines. Finally, we apply our method to a real-world observational case study to demonstrate the value of identifying dose-dependent causal effects.

JAIR Journal 2022 Journal Article

A Metric Space for Point Process Excitations

Myrl G. Marmarelis
Greg Ver Steeg
Aram Galstyan

A multivariate Hawkes process enables self- and cross-excitations through a triggering matrix that behaves like an asymmetrical covariance structure, characterizing pairwise interactions between the event types. Full-rank estimation of all interactions is often infeasible in empirical settings. Models that specialize on a spatiotemporal application alleviate this obstacle by exploiting spatial locality, allowing the dyadic relationships between events to depend only on separation in time and relative distances in real Euclidean space. Here we generalize this framework to any multivariate Hawkes process, and harness it as a vessel for embedding arbitrary event types in a hidden metric space. Specifically, we propose a Hidden Hawkes Geometry (HHG) model to uncover the hidden geometry between event excitations in a multivariate point process. The low dimensionality of the embedding regularizes the structure of the inferred interactions. We develop a number of estimators and validate the model by conducting several experiments. In particular, we investigate regional infectivity dynamics of COVID-19 in an early South Korean record and recent Los Angeles confirmed cases. By additionally performing synthetic experiments on short records as well as explorations into options markets and the Ebola epidemic, we demonstrate that learning the embedding alongside a point process uncovers salient interactions in a broad range of applications.

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ICLR Conference 2022 Conference Paper

Improving Mutual Information Estimation with Annealed and Energy-Based Bounds

Rob Brekelmans
Sicong Huang 0001
Marzyeh Ghassemi
Greg Ver Steeg
Roger B. Grosse
Alireza Makhzani

Mutual information (MI) is a fundamental quantity in information theory and machine learning. However, direct estimation of MI is intractable, even if the true joint probability density for the variables of interest is known, as it involves estimating a potentially high-dimensional log partition function. In this work, we present a unifying view of existing MI bounds from the perspective of importance sampling, and propose three novel bounds based on this approach. Since a tight MI bound without density information requires a sample size exponential in the true MI, we assume either a single marginal or the full joint density information is known. In settings where the full joint density is available, we propose Multi-Sample Annealed Importance Sampling (AIS) bounds on MI, which we demonstrate can tightly estimate large values of MI in our experiments. In settings where only a single marginal distribution is known, we propose Generalized IWAE (GIWAE) and MINE-AIS bounds. Our GIWAE bound unifies variational and contrastive bounds in a single framework that generalizes InfoNCE, IWAE, and Barber-Agakov bounds. Our MINE-AIS method improves upon existing energy-based methods such as MINE-DV and MINE-F by directly optimizing a tighter lower bound on MI. MINE-AIS uses MCMC sampling to estimate gradients for training and Multi-Sample AIS for evaluating the bound. Our methods are particularly suitable for evaluating MI in deep generative models, since explicit forms of the marginal or joint densities are often available. We evaluate our bounds on estimating the MI of VAEs and GANs trained on the MNIST and CIFAR datasets, and showcase significant gains over existing bounds in these challenging settings with high ground truth MI.

AAAI Conference 2021 Conference Paper

Controllable Guarantees for Fair Outcomes via Contrastive Information Estimation

Umang Gupta
Aaron M Ferber
Bistra Dilkina
Greg Ver Steeg

Controlling bias in training datasets is vital for ensuring equal treatment, or parity, between different groups in downstream applications. A naive solution is to transform the data so that it is statistically independent of group membership, but this may throw away too much information when a reasonable compromise between fairness and accuracy is desired. Another common approach is to limit the ability of a particular adversary who seeks to maximize parity. Unfortunately, representations produced by adversarial approaches may still retain biases as their efficacy is tied to the complexity of the adversary used during training. To this end, we theoretically establish that by limiting the mutual information between representations and protected attributes, we can assuredly control the parity of any downstream classifier. We demonstrate an effective method for controlling parity through mutual information based on contrastive information estimators and show that they outperform approaches that rely on variational bounds based on complex generative models. We test our approach on UCI Adult and Heritage Health datasets and demonstrate that our approach provides more informative representations across a range of desired parity thresholds while providing strong theoretical guarantees on the parity of any downstream algorithm.

ICLR Conference 2021 Conference Paper

Graph Traversal with Tensor Functionals: A Meta-Algorithm for Scalable Learning

Elan Sopher Markowitz
Keshav Balasubramanian
Mehrnoosh Mirtaheri
Sami Abu-El-Haija
Bryan Perozzi
Greg Ver Steeg
Aram Galstyan

Graph Representation Learning (GRL) methods have impacted fields from chemistry to social science. However, their algorithmic implementations are specialized to specific use-cases e.g. "message passing" methods are run differently from "node embedding" ones. Despite their apparent differences, all these methods utilize the graph structure, and therefore, their learning can be approximated with stochastic graph traversals. We propose Graph Traversal via Tensor Functionals (GTTF), a unifying meta-algorithm framework for easing the implementation of diverse graph algorithms and enabling transparent and efficient scaling to large graphs. GTTF is founded upon a data structure (stored as a sparse tensor) and a stochastic graph traversal algorithm (described using tensor operations). The algorithm is a functional that accept two functions, and can be specialized to obtain a variety of GRL models and objectives, simply by changing those two functions. We show for a wide class of methods, our algorithm learns in an unbiased fashion and, in expectation, approximates the learning as if the specialized implementations were run directly. With these capabilities, we scale otherwise non-scalable methods to set state-of-the-art on large graph datasets while being more efficient than existing GRL libraries -- with only a handful of lines of code for each method specialization.

NeurIPS Conference 2021 Conference Paper

Hamiltonian Dynamics with Non-Newtonian Momentum for Rapid Sampling

Greg Ver Steeg
Aram Galstyan

Sampling from an unnormalized probability distribution is a fundamental problem in machine learning with applications including Bayesian modeling, latent factor inference, and energy-based model training. After decades of research, variations of MCMC remain the default approach to sampling despite slow convergence. Auxiliary neural models can learn to speed up MCMC, but the overhead for training the extra model can be prohibitive. We propose a fundamentally different approach to this problem via a new Hamiltonian dynamics with a non-Newtonian momentum. In contrast to MCMC approaches like Hamiltonian Monte Carlo, no stochastic step is required. Instead, the proposed deterministic dynamics in an extended state space exactly sample the target distribution, specified by an energy function, under an assumption of ergodicity. Alternatively, the dynamics can be interpreted as a normalizing flow that samples a specified energy model without training. The proposed Energy Sampling Hamiltonian (ESH) dynamics have a simple form that can be solved with existing ODE solvers, but we derive a specialized solver that exhibits much better performance. ESH dynamics converge faster than their MCMC competitors enabling faster, more stable training of neural network energy models.

NeurIPS Conference 2021 Conference Paper

Implicit SVD for Graph Representation Learning

Sami Abu-El-Haija
Hesham Mostafa
Marcel Nassar
Valentino Crespi
Greg Ver Steeg
Aram Galstyan

Recent improvements in the performance of state-of-the-art (SOTA) methods for Graph Representational Learning (GRL) have come at the cost of significant computational resource requirements for training, e. g. , for calculating gradients via backprop over many data epochs. Meanwhile, Singular Value Decomposition (SVD) can find closed-form solutions to convex problems, using merely a handful of epochs. In this paper, we make GRL more computationally tractable for those with modest hardware. We design a framework that computes SVD of *implicitly* defined matrices, and apply this framework to several GRL tasks. For each task, we derive first-order approximation of a SOTA model, where we design (expensive-to-store) matrix $\mathbf{M}$ and train the model, in closed-form, via SVD of $\mathbf{M}$, without calculating entries of $\mathbf{M}$. By converging to a unique point in one step, and without calculating gradients, our models show competitive empirical test performance over various graphs such as article citation and biological interaction networks. More importantly, SVD can initialize a deeper model, that is architected to be non-linear almost everywhere, though behaves linearly when its parameters reside on a hyperplane, onto which SVD initializes. The deeper model can then be fine-tuned within only a few epochs. Overall, our algorithm trains hundreds of times faster than state-of-the-art methods, while competing on test empirical performance. We open-source our implementation at: https: //github. com/samihaija/isvd

NeurIPS Conference 2021 Conference Paper

Information-theoretic generalization bounds for black-box learning algorithms

Hrayr Harutyunyan
Maxim Raginsky
Greg Ver Steeg
Aram Galstyan

We derive information-theoretic generalization bounds for supervised learning algorithms based on the information contained in predictions rather than in the output of the training algorithm. These bounds improve over the existing information-theoretic bounds, are applicable to a wider range of algorithms, and solve two key challenges: (a) they give meaningful results for deterministic algorithms and (b) they are significantly easier to estimate. We show experimentally that the proposed bounds closely follow the generalization gap in practical scenarios for deep learning.

UAI Conference 2021 Conference Paper

q-Paths: Generalizing the geometric annealing path using power means

Vaden Masrani
Rob Brekelmans
Thang Bui
Frank Nielsen
Aram Galstyan
Greg Ver Steeg
Frank Wood

Many common machine learning methods involve the geometric annealing path, a sequence of intermediate densities between two distributions of interest constructed using the geometric average. While alternatives such as the moment-averaging path have demonstrated performance gains in some settings, their practical applicability remains limited by exponential family endpoint assumptions and a lack of closed form energy function. In this work, we introduce $q$-paths, a family of paths which is derived from a generalized notion of the mean, includes the geometric and arithmetic mixtures as special cases, and admits a simple closed form involving the deformed logarithm function from nonextensive thermodynamics. Following previous analysis of the geometric path, we interpret our $q$-paths as corresponding to a $q$-exponential family of distributions, and provide a variational representation of intermediate densities as minimizing a mixture of $\alpha$-divergences to the endpoints. We show that small deviations away from the geometric path yield empirical gains for Bayesian inference using Sequential Monte Carlo and generative model evaluation using Annealed Importance Sampling.

ICML Conference 2020 Conference Paper

All in the Exponential Family: Bregman Duality in Thermodynamic Variational Inference

Rob Brekelmans
Vaden Masrani
Frank Wood
Greg Ver Steeg
Aram Galstyan

The recently proposed Thermodynamic Variational Objective (TVO) leverages thermodynamic integration to provide a family of variational inference objectives, which both tighten and generalize the ubiquitous Evidence Lower Bound (ELBO). However, the tightness of TVO bounds was not previously known, an expensive grid search was used to choose a “schedule” of intermediate distributions, and model learning suffered with ostensibly tighter bounds. In this work, we propose an exponential family interpretation of the geometric mixture curve underlying the TVO and various path sampling methods, which allows us to characterize the gap in TVO likelihood bounds as a sum of KL divergences. We propose to choose intermediate distributions using equal spacing in the moment parameters of our exponential family, which matches grid search performance and allows the schedule to adaptively update over the course of training. Finally, we derive a doubly reparameterized gradient estimator which improves model learning and allows the TVO to benefit from more refined bounds. To further contextualize our contributions, we provide a unified framework for understanding thermodynamic integration and the TVO using Taylor series remainders.

ICML Conference 2020 Conference Paper

Improving generalization by controlling label-noise information in neural network weights

Hrayr Harutyunyan
Kyle Reing
Greg Ver Steeg
Aram Galstyan

In the presence of noisy or incorrect labels, neural networks have the undesirable tendency to memorize information about the noise. Standard regularization techniques such as dropout, weight decay or data augmentation sometimes help, but do not prevent this behavior. If one considers neural network weights as random variables that depend on the data and stochasticity of training, the amount of memorized information can be quantified with the Shannon mutual information between weights and the vector of all training labels given inputs, $I(w; \mathbf{y} \mid \mathbf{x})$. We show that for any training algorithm, low values of this term correspond to reduction in memorization of label-noise and better generalization bounds. To obtain these low values, we propose training algorithms that employ an auxiliary network that predicts gradients in the final layers of a classifier without accessing labels. We illustrate the effectiveness of our approach on versions of MNIST, CIFAR-10, and CIFAR-100 corrupted with various noise models, and on a large-scale dataset Clothing1M that has noisy labels.

AAAI Conference 2020 Conference Paper

Invariant Representations through Adversarial Forgetting

Ayush Jaiswal
Daniel Moyer
Greg Ver Steeg
Wael AbdAlmageed
Premkumar Natarajan

We propose a novel approach to achieving invariance for deep neural networks in the form of inducing amnesia to unwanted factors of data through a new adversarial forgetting mechanism. We show that the forgetting mechanism serves as an information-bottleneck, which is manipulated by the adversarial training to learn invariance to unwanted factors. Empirical results show that the proposed framework achieves stateof-the-art performance at learning invariance in both nuisance and bias settings on a diverse collection of datasets and tasks.

AAAI Conference 2020 Conference Paper

Modeling Dialogues with Hashcode Representations: A Nonparametric Approach

Sahil Garg
Irina Rish
Guillermo Cecchi
Palash Goyal
Sarik Ghazarian
Shuyang Gao
Greg Ver Steeg
Aram Galstyan

We propose a novel dialogue modeling framework, the ﬁrstever nonparametric kernel functions based approach for dialogue modeling, which learns hashcodes as text representations; unlike traditional deep learning models, it handles well relatively small datasets, while also scaling to large ones. We also derive a novel lower bound on mutual information, used as a model-selection criterion favoring representations with better alignment between the utterances of participants in a collaborative dialogue setting, as well as higher predictability of the generated responses. As demonstrated on three real-life datasets, including prominently psychotherapy sessions, the proposed approach signiﬁcantly outperforms several state-ofart neural network based dialogue systems, both in terms of computational efﬁciency, reducing training time from days or weeks to hours, and the response quality, achieving an order of magnitude improvement over competitors in frequency of being chosen as the best model by human evaluators.

NeurIPS Conference 2019 Conference Paper

Exact Rate-Distortion in Autoencoders via Echo Noise

Rob Brekelmans
Daniel Moyer
Aram Galstyan
Greg Ver Steeg

Compression is at the heart of effective representation learning. However, lossy compression is typically achieved through simple parametric models like Gaussian noise to preserve analytic tractability, and the limitations this imposes on learning are largely unexplored. Further, the Gaussian prior assumptions in models such as variational autoencoders (VAEs) provide only an upper bound on the compression rate in general. We introduce a new noise channel, Echo noise, that admits a simple, exact expression for mutual information for arbitrary input distributions. The noise is constructed in a data-driven fashion that does not require restrictive distributional assumptions. With its complex encoding mechanism and exact rate regularization, Echo leads to improved bounds on log-likelihood and dominates beta-VAEs across the achievable range of rate-distortion trade-offs. Further, we show that Echo noise can outperform flow-based methods without the need to train additional distributional transformations.

NeurIPS Conference 2019 Conference Paper

Fast structure learning with modular regularization

Greg Ver Steeg
Hrayr Harutyunyan
Daniel Moyer
Aram Galstyan

Estimating graphical model structure from high-dimensional and undersampled data is a fundamental problem in many scientific fields. Existing approaches, such as GLASSO, latent variable GLASSO, and latent tree models, suffer from high computational complexity and may impose unrealistic sparsity priors in some cases. We introduce a novel method that leverages a newly discovered connection between information-theoretic measures and structured latent factor models to derive an optimization objective which encourages modular structures where each observed variable has a single latent parent. The proposed method has linear stepwise computational complexity w. r. t. the number of observed variables. Our experiments on synthetic data demonstrate that our approach is the only method that recovers modular structure better as the dimensionality increases. We also use our approach for estimating covariance structure for a number of real-world datasets and show that it consistently outperforms state-of-the-art estimators at a fraction of the computational cost. Finally, we apply the proposed method to high-resolution fMRI data (with more than 10^5 voxels) and show that it is capable of extracting meaningful patterns.

AAAI Conference 2019 Conference Paper

Kernelized Hashcode Representations for Relation Extraction

Sahil Garg
Aram Galstyan
Greg Ver Steeg
Irina Rish
Guillermo Cecchi
Shuyang Gao

Kernel methods have produced state-of-the-art results for a number of NLP tasks such as relation extraction, but suffer from poor scalability due to the high cost of computing kernel similarities between natural language structures. A recently proposed technique, kernelized locality-sensitive hashing (KLSH), can significantly reduce the computational cost, but is only applicable to classifiers operating on kNN graphs. Here we propose to use random subspaces of KLSH codes for efficiently constructing an explicit representation of NLP structures suitable for general classification methods. Further, we propose an approach for optimizing the KLSH model for classification problems by maximizing an approximation of mutual information between the KLSH codes (feature vectors) and the class labels. We evaluate the proposed approach on biomedical relation extraction datasets, and observe significant and robust improvements in accuracy w. r. t. state-ofthe-art classifiers, along with drastic (orders-of-magnitude) speedup compared to conventional kernel methods.

ICML Conference 2019 Conference Paper

MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing

Sami Abu-El-Haija
Bryan Perozzi
Amol Kapoor
Nazanin Alipourfard
Kristina Lerman
Hrayr Harutyunyan
Greg Ver Steeg
Aram Galstyan

Existing popular methods for semi-supervised learning with Graph Neural Networks (such as the Graph Convolutional Network) provably cannot learn a general class of neighborhood mixing relationships. To address this weakness, we propose a new model, MixHop, that can learn these relationships, including difference operators, by repeatedly mixing feature representations of neighbors at various distances. MixHop requires no additional memory or computational complexity, and outperforms on challenging baselines. In addition, we propose sparsity regularization that allows us to visualize how the network prioritizes neighborhood information across different graph datasets. Our analysis of the learned architectures reveals that neighborhood mixing varies per datasets.

UAI Conference 2018 Conference Paper

A Forest Mixture Bound for Block-Free Parallel Inference

Neal Lawton
Greg Ver Steeg
Aram Galstyan

way to perform parallel inference in such models, or do we have to resort to the serial coordinate algorithm? Coordinate ascent variational inference is an important algorithm for inference in probabilistic models, but it is slow because it updates only a single variable at a time. Block coordinate methods perform inference faster by updating blocks of variables in parallel. However, the speed and convergence of these algorithms depends on how the variables are partitioned into blocks. In this paper, we give a convergent parallel algorithm for inference in deep exponential families that doesn’t require the variables to be partitioned into blocks. We achieve this by lower bounding the ELBO by a new objective we call the forest mixture bound (FM bound) that separates the inference problem for variables within a hidden layer. We apply this to the simple case when all random variables are Gaussian and show empirically that the algorithm converges faster for models that are inherently more forest-like. Block methods provide one avenue for parallel inference. These algorithms work by first partitioning the latent variables into a collection of blocks, and then iteratively updating a variable from each block in parallel. However, the speed (as in MCMC methods [Terenin et al. , 2015]) or convergence (as in Hogwild methods [Recht et al. , 2011]) of the resulting algorithm will depend on how the variables are blocked, and finding a good choice of blocking for an arbitrary model can be difficult.

NeurIPS Conference 2018 Conference Paper

Invariant Representations without Adversarial Training

Daniel Moyer
Shuyang Gao
Rob Brekelmans
Aram Galstyan
Greg Ver Steeg

Representations of data that are invariant to changes in specified factors are useful for a wide range of problems: removing potential biases in prediction problems, controlling the effects of covariates, and disentangling meaningful factors of variation. Unfortunately, learning representations that exhibit invariance to arbitrary nuisance factors yet remain useful for other tasks is challenging. Existing approaches cast the trade-off between task performance and invariance in an adversarial way, using an iterative minimax optimization. We show that adversarial training is unnecessary and sometimes counter-productive; we instead cast invariant representation learning as a single information-theoretic objective that can be directly optimized. We demonstrate that this approach matches or exceeds performance of state-of-the-art adversarial approaches for learning fair representations and for generative modeling with controllable transformations.

IJCAI Conference 2017 Conference Paper

Sifting Common Information from Many Variables

Greg Ver Steeg
Shuyang Gao
Kyle Reing
Aram Galstyan

Measuring the relationship between any pair of variables is a rich and active area of research that is central to scientific practice. In contrast, characterizing the common information among any group of variables is typically a theoretical exercise with few practical methods for high-dimensional data. A promising solution would be a multivariate generalization of the famous Wyner common information, but this approach relies on solving an apparently intractable optimization problem. We leverage the recently introduced information sieve decomposition to formulate an incremental version of the common information problem that admits a simple fixed point solution, fast convergence, and complexity that is linear in the number of variables. This scalable approach allows us to demonstrate the usefulness of common information in high-dimensional learning problems. The sieve outperforms standard methods on dimensionality reduction tasks, solves a blind source separation problem that cannot be solved with ICA, and accurately recovers structure in brain imaging data.

IJCAI Conference 2017 Conference Paper

Unsupervised Learning via Total Correlation Explanation

Greg Ver Steeg

Learning by children and animals occurs effortlessly and largely without obvious supervision. Successes in automating supervised learning have not translated to the more ambiguous realm of unsupervised learning where goals and labels are not provided. Barlow (1961) suggested that the signal that brains leverage for unsupervised learning is dependence, or redundancy, in the sensory environment. Dependence can be characterized using the information-theoretic multivariate mutual information measure called total correlation. The principle of Total Cor-relation Ex-planation (CorEx) is to learn representations of data that "explain" as much dependence in the data as possible. We review some manifestations of this principle along with successes in unsupervised learning problems across diverse domains including human behavior, biology, and language.

ICML Conference 2016 Conference Paper

The Information Sieve

Greg Ver Steeg
Aram Galstyan

We introduce a new framework for unsupervised learning of representations based on a novel hierarchical decomposition of information. Intuitively, data is passed through a series of progressively fine-grained sieves. Each layer of the sieve recovers a single latent factor that is maximally informative about multivariate dependence in the data. The data is transformed after each pass so that the remaining unexplained information trickles down to the next layer. Ultimately, we are left with a set of latent factors explaining all the dependence in the original data and remainder information consisting of independent noise. We present a practical implementation of this framework for discrete variables and apply it to a variety of fundamental tasks in unsupervised learning including independent component analysis, lossy and lossless compression, and predicting missing values in data.

NeurIPS Conference 2016 Conference Paper

Variational Information Maximization for Feature Selection

Shuyang Gao
Greg Ver Steeg
Aram Galstyan

Feature selection is one of the most fundamental problems in machine learning. An extensive body of work on information-theoretic feature selection exists which is based on maximizing mutual information between subsets of features and class labels. Practical methods are forced to rely on approximations due to the difficulty of estimating mutual information. We demonstrate that approximations made by existing methods are based on unrealistic assumptions. We formulate a more flexible and general class of assumptions based on variational distributions and use them to tractably generate lower bounds for mutual information. These bounds define a novel information-theoretic framework for feature selection, which we prove to be optimal under tree graphical models with proper choice of variational distributions. Our experiments demonstrate that the proposed method strongly outperforms existing information-theoretic feature selection approaches.

UAI Conference 2015 Conference Paper

Estimating Mutual Information by Local Gaussian Approximation

Shuyang Gao
Greg Ver Steeg
Aram Galstyan

Estimating mutual information (MI) from samples is a fundamental problem in statistics, machine learning, and data analysis. Recently it was shown that a popular class of non-parametric MI estimators perform very poorly for strongly dependent variables and have sample complexity that scales exponentially with the true MI. This undesired behavior was attributed to the reliance of those estimators on local uniformity of the underlying (and unknown) probability density function. Here we present a novel semi-parametric estimator of mutual information, where at each sample point, densities are locally approximated by a Gaussians distribution. We demonstrate that the estimator is asymptotically unbiased. We also show that the proposed estimator has a superior performance compared to several baselines, and is able to accurately measure relationship strengths over many orders of magnitude.

ICML Conference 2014 Conference Paper

Demystifying Information-Theoretic Clustering

Greg Ver Steeg
Aram Galstyan
Fei Sha
Simon DeDeo

We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based on maximizing mutual information between data and cluster labels. We demonstrate that this intuition suffers from a fundamental conceptual flaw that causes clustering performance to deteriorate as the amount of data increases. Instead, we return to the axiomatic foundations of information theory to define a meaningful clustering measure based on the notion of consistency under coarse-graining for finite data.

NeurIPS Conference 2014 Conference Paper

Discovering Structure in High-Dimensional Data Through Correlation Explanation

Greg Ver Steeg
Aram Galstyan

We introduce a method to learn a hierarchy of successively more abstract representations of complex data based on optimizing an information-theoretic objective. Intuitively, the optimization searches for a set of latent factors that best explain the correlations in the data as measured by multivariate mutual information. The method is unsupervised, requires no model assumptions, and scales linearly with the number of variables which makes it an attractive approach for very high dimensional systems. We demonstrate that Correlation Explanation (CorEx) automatically discovers meaningful structure for data from diverse sources including personality tests, DNA, and human language.

AAAI Conference 2014 Conference Paper

Where and Why Users “Check In”

Yoon-Sik Cho
Greg Ver Steeg
Aram Galstyan

The emergence of location based social network (LBSN) services makes it possible to study individuals’ mobility patterns at a fine-grained level and to see how they are impacted by social factors. In this study we analyze the check-in patterns in LBSN and observe significant temporal clustering of check-in activities. We explore how self-reinforcing behaviors, social factors, and exogenous effects contribute to this clustering and introduce a framework to distinguish these effects at the level of individual check-ins for both users and venues. Using check-in data from three major cities, we show not only that our model can improve prediction of future check-ins, but also that disentangling of different factors allows us to infer meaningful properties of different venues.

UAI Conference 2011 Conference Paper

A Sequence of Relaxation Constraining Hidden Variable Models

Greg Ver Steeg
Aram Galstyan

Many widely studied graphical models with latent variables lead to nontrivial constraints on the distribution of the observed variables. Inspired by the Bell inequalities in quantum mechanics, we refer to any linear inequality whose violation rules out some latent variable model as a "hidden variable test" for that model. Our main contribution is to introduce a sequence of relaxations which provides progressively tighter hidden variable tests. We demonstrate applicability to mixtures of sequences of i.i.d. variables, Bell inequalities, and homophily models in social networks. For the last, we demonstrate that our method provides a test that is able to rule out latent homophily as the sole explanation for correlations on a real social network that are known to be due to influence.

UAI Conference 2011 Conference Paper

Statistical Mechanics of Semi-Supervised Clustering in Sparse Graphs (Abstract)

Greg Ver Steeg
Aram Galstyan
Armen E. Allahverdyan

The problem of detecting modules, or clusters, in networks has recently attracted a considerable interest both in statistical physics and computer science communities. In addition to algorithmic development, recent research has addressed the feasibility of detecting clusters, assuming they are present in the network.