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High-dimensional data must be highly structured to be learnable. Although the compositional and hierarchical nature of data is often put forward to explain learnability, quantitative measurements establishing these properties are scarce.…
A statistical model of protein families, called profile conditional random fields (CRFs), is proposed. This model may be regarded as an integration of the profile hidden Markov model (HMM) and the Finkelstein-Reva (FR) theory of protein…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
This tutorial overviews the state of the art in learning models over relational databases and makes the case for a first-principles approach that exploits recent developments in database research. The input to learning classification and…
Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…
Most real-world datasets consist of a natural hierarchy between classes or an inherent label structure that is either already available or can be constructed cheaply. However, most existing representation learning methods ignore this…
In this work, we analyze the nonequilibrium thermodynamics of a class of neural networks known as Restricted Boltzmann Machines (RBMs) in the context of unsupervised learning. We show how the network is described as a discrete Markov…
The ubiquitous role of the cyber-infrastructures, such as the WWW, provides myriad opportunities for machine learning and its broad spectrum of application domains taking advantage of digital communication. Pattern classification and…
Networks, which represent agents and interactions between them, arise in myriad applications throughout the sciences, engineering, and even the humanities. To understand large-scale structure in a network, a common task is to cluster a…
Clustered data, which arise when observations are nested within groups, are incredibly common in clinical, education, and social science research. Traditionally, a linear mixed model, which includes random effects to account for…
We consider the analysis of high dimensional data given in the form of a matrix with columns consisting of observations and rows consisting of features. Often the data is such that the observations do not reside on a regular grid, and the…
Most real-world networks evolve over time. Existing literature proposes models for dynamic networks that are either unlabeled or assumed to have a single membership structure. On the other hand, a new family of Mixed Membership Stochastic…
Restricted Boltzmann machines (RBMs) are endowed with the universal power of modeling (binary) joint distributions. Meanwhile, as a result of their confining network structure, training RBMs confronts less difficulties (compared with more…
The last decades have not only been characterized by an explosive growth of data, but also an increasing appreciation of data as a valuable resource. Their value comes with the ability to extract meaningful patterns that are of economic,…
From biological organs to soft robotics, highly deformable materials are essential components of natural and engineered systems. These highly deformable materials can have heterogeneous material properties, and can experience heterogeneous…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…
Unsupervised models can provide supplementary soft constraints to help classify new target data under the assumption that similar objects in the target set are more likely to share the same class label. Such models can also help detect…
Restricted Boltzmann Machines (RBMs) are powerful tools for modeling complex systems and extracting insights from data, but their training is hindered by the slow mixing of Markov Chain Monte Carlo (MCMC) processes, especially with highly…
A new approach to maximum likelihood learning of discrete graphical models and RBM in particular is introduced. Our method, Perturb and Descend (PD) is inspired by two ideas (I) perturb and MAP method for sampling (II) learning by…
Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life. One approach to representing…