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This paper addresses the inference of spatial dependence in the context of a recently proposed framework. More specifically, the paper focuses on the estimation of model parameters for a class of generalized Gibbs random fields, i.e.,…
Bayesian inference of Gibbs random fields (GRFs) is often referred to as a doubly intractable problem, since the likelihood function is intractable. The exploration of the posterior distribution of such models is typically carried out with…
This thesis studies two problems in modern statistics. First, we study selective inference, or inference for hypothesis that are chosen after looking at the data. The motiving application is inference for regression coefficients selected by…
The hidden Markov model (HMM) is a fundamental tool for sequence modeling that cleanly separates the hidden state from the emission structure. However, this separation makes it difficult to fit HMMs to large datasets in modern NLP, and they…
We propose a Bayesian nonparametric mixture model for prediction- and information extraction tasks with an efficient inference scheme. It models categorical-valued time series that exhibit dynamics from multiple underlying patterns (e.g.…
Graphical models trained using maximum likelihood are a common tool for probabilistic inference of marginal distributions. However, this approach suffers difficulties when either the inference process or the model is approximate. In this…
While convolutional neural networks (CNNs) trained by back-propagation have seen unprecedented success at semantic segmentation tasks, they are known to struggle on out-of-distribution data. Markov random fields (MRFs) on the other hand,…
In this work we provide a theoretical framework for structured prediction that generalizes the existing theory of surrogate methods for binary and multiclass classification based on estimating conditional probabilities with smooth convex…
Hidden Markov models (HMMs) are flexible tools for clustering dependent data coming from unknown populations, allowing nonparametric modelling of the population densities. Identifiability fails when the data is in fact independent and…
We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…
Electronic structure methods offer in principle accurate predictions of molecular properties, however, their applicability is limited by computational costs. Empirical methods are cheaper, but come with inherent approximations and are…
We introduce a new surrogate loss function called orbit loss in the structured prediction framework, which has good theoretical and practical advantages. While the orbit loss is not convex, it has a simple analytical gradient and a simple…
This is a technical report which explores the estimation methodologies on hyper-parameters in Markov Random Field and Gaussian Hidden Markov Random Field. In first section, we briefly investigate a theoretical framework on…
We consider the problem of inferring constraints on a high-dimensional parameter space with a computationally expensive likelihood function. We propose a machine learning algorithm that maps out the Frequentist confidence limit on parameter…
The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a…
Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) provide useful tools for modeling dynamical systems. They are particularly useful for representing the topology of environments such as road networks…
High-dimensional and sparse (HiDS) matrices are omnipresent in a variety of big data-related applications. Latent factor analysis (LFA) is a typical representation learning method that extracts useful yet latent knowledge from HiDS matrices…
Restricted Boltzmann Machines (RBMs) are a common family of undirected graphical models with latent variables. An RBM is described by a bipartite graph, with all observed variables in one layer and all latent variables in the other. We…
This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep…
We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…