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Mixtures of Mallows models are a popular generative model for ranking data coming from a heterogeneous population. They have a variety of applications including social choice, recommendation systems and natural language processing. Here we…

We address the problem of analyzing sets of noisy time-varying signals that all report on the same process but confound straightforward analyses due to complex inter-signal heterogeneities and measurement artifacts. In particular we…

Recent work has discussed the importance of multiplicative closure for the Markov models used in phylogenetics. For continuous-time Markov chains, a sufficient condition for multiplicative closure of a model class is ensured by demanding…

We study the frontier between learnable and unlearnable hidden Markov models (HMMs). HMMs are flexible tools for clustering dependent data coming from unknown populations. The model parameters are known to be fully identifiable (up to…

We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a…

We study the problem of learning mixtures of low-rank models, i.e. reconstructing multiple low-rank matrices from unlabelled linear measurements of each. This problem enriches two widely studied settings -- low-rank matrix sensing and mixed…

We consider the filtering of continuous-time finite-state hidden Markov models, where the rate and observation matrices depend on unknown time-dependent parameters, for which no prior or stochastic model is available. We quantify and…

We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…

We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test…

We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…

We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their relative merits and limitations remain…

We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…

This work focuses on the problem of unraveling nonlinearly mixed latent components in an unsupervised manner. The latent components are assumed to reside in the probability simplex, and are transformed by an unknown post-nonlinear mixing…

In singular models, the optimal set of parameters forms an analytic set with singularities and classical statistical inference cannot be applied to such models. This is significant for deep learning as neural networks are singular and thus…

Markov networks are widely used in many Machine Learning applications including natural language processing, computer vision, and bioinformatics . Learning Markov networks have many complications ranging from intractable computations…

Given a finite and noisy dataset generated with a closed-form mathematical model, when is it possible to learn the true generating model from the data alone? This is the question we investigate here. We show that this model-learning problem…

We present a new algorithm for identifying the transition and emission probabilities of a hidden Markov model (HMM) from the emitted data. Expectation-maximization becomes computationally prohibitive for long observation records, which are…

While discrete latent variable models have had great success in self-supervised learning, most models assume that frames are independent. Due to the segmental nature of phonemes in speech perception, modeling dependencies among latent…

This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…

We provide high-probability sample complexity guarantees for exact structure recovery and accurate predictive learning using noise-corrupted samples from an acyclic (tree-shaped) graphical model. The hidden variables follow a…