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In the hidden Markov process, there is a possibility that two different transition matrices for hidden and observed variables yield the same stochastic behavior for the observed variables. Since such two transition matrices cannot be…

A hidden Markov model (HMM) is said to have path-mergeable states if for any two states i,j there exists a word w and state k such that it is possible to transition from both i and j to k while emitting w. We show that for a finite HMM with…

This work addresses the problem of identifiability, that is, the question of whether parameters can be recovered from data, for linear compartmental models. Using standard differential algebra techniques, the question of whether a given…

This paper studies parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters. Fixing values for all parameters…

Relational Markov Decision Processes are a useful abstraction for complex reinforcement learning problems and stochastic planning problems. Recent work developed representation schemes and algorithms for planning in such problems using the…

We revisit the problem of perturbing a large, i.i.d. random matrix by a finite rank error. It is known that when elements of the i.i.d. matrix have finite fourth moment, then the outlier eigenvalues of the perturbed matrix are close to the…

Let $M=(E,{\cal I})$ be a matroid. A {\em $k$-truncation} of $M$ is a matroid {$M'=(E,{\cal I}')$} such that for any $A\subseteq E$, $A\in {\cal I}'$ if and only if $|A|\leq k$ and $A\in {\cal I}$. Given a linear representation of $M$ we…

We study parameter identification problems in a structured population model without mutations. Given measurements of the total population size or critical points of the population, we aim to recover its growth rate, death rate or initial…

In this article almost semi-continuous processes with stationary independent increments on a finite irreducible Markov chain are considered. For these processes the components of matrix factorization identity are concretely defined. On the…

The technological applications of hidden Markov models have been extremely diverse and successful, including natural language processing, gesture recognition, gene sequencing, and Kalman filtering of physical measurements. HMMs are highly…

The problem of completing high-dimensional matrices from a limited set of observations arises in many big data applications, especially, recommender systems. Existing matrix completion models generally follow either a memory- or a…

Representation learning is a fundamental building block for analyzing entities in a database. While the existing embedding learning methods are effective in various data mining problems, their applicability is often limited because these…

Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution, and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix $c>0$ and $p>0$. Let $A_n$ be the adjacency matrix…

The quantum separability problem consists in deciding whether a bipartite density matrix is entangled or separable. In this work, we propose a machine learning pipeline for finding approximate solutions for this NP-hard problem in…

The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completion problem are based on singular value thresholding and…

Let $K$ be a number field, let $A$ be a finite-dimensional $K$-algebra, let $\mathrm{J}(A)$ denote the Jacobson radical of $A$, and let $\Lambda$ be an $\mathcal{O}_{K}$-order in $A$. Suppose that each simple component of the semisimple…

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…

We consider two basic algorithmic problems concerning tuples of (skew-)symmetric matrices. The first problem asks to decide, given two tuples of (skew-)symmetric matrices $(B_1, \dots, B_m)$ and $(C_1, \dots, C_m)$, whether there exists an…

We consider the parameter estimation of Markov chain when the unknown transition matrix belongs to an exponential family of transition matrices. Then, we show that the sample mean of the generator of the exponential family is an…

In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs---labeled directed graphs---and predicting missing relationships---labeled edges. State-of-the-art…