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Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great…
Coordinated base station (BS) transmission has attracted much interest for its potential to increase the capacity of wireless networks. Yet at the same time, the achievable sum-rate with single-cell processing (SCP) scales optimally with…
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The…
Communication costs, resulting from synchronization requirements during learning, can greatly slow down many parallel machine learning algorithms. In this paper, we present a parallel Markov chain Monte Carlo (MCMC) algorithm in which…
Reject inference comprises techniques to infer the possible repayment behavior of rejected cases. In this paper, we model credit in a brand new view by capturing the sequential pattern of interactions among multiple stages of loan business…
Given a graph $G=(V,E)$ and a set of terminal vertices $T$ we say that a superset $S$ of $T$ is $T$-connecting if $S$ induces a connected graph, and $S$ is minimal if no strict subset of $S$ is $T$-connecting. In this paper we prove that…
This paper surveys various results about Markov chains on general (non-countable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which…
We propose an approach to lossy source coding, utilizing ideas from Gibbs sampling, simulated annealing, and Markov Chain Monte Carlo (MCMC). The idea is to sample a reconstruction sequence from a Boltzmann distribution associated with an…
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…
Recent work has revealed many intriguing empirical phenomena in neural network training, despite the poorly understood and highly complex loss landscapes and training dynamics. One of these phenomena, Linear Mode Connectivity (LMC), has…
The perceived advantage of machine learning (ML) models is that they are flexible and can incorporate a large number of features. However, many of these are typically correlated or dependent, and incorporating all of them can hinder model…
We consider conditional exact tests of factor effects in designed experiments for discrete response variables. Similarly to the analysis of contingency tables, a Markov chain Monte Carlo method can be used for performing exact tests, when…
In some cases, computational benefit can be gained by exploring the hyper parameter space using a deterministic set of grid points instead of a Markov chain. We view this as a numerical integration problem and make three unique…
We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the…
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…
Base station cooperation can exploit knowledge of the users' channel state information (CSI) at the transmitters to manage co-channel interference. Users have to feedback CSI of the desired and interfering channels using finite-bandwidth…
It is known that a Markov basis of the binary graph model of a graph $G$ corresponds to a set of binomial generators of cut ideals $I_{\widehat{G}}$ of the suspension $\widehat{G}$ of $G$. In this paper, we give another application of cut…
One of the major problems in adaptive filtering is the problem of system identification. It has been studied extensively due to its immense practical importance in a variety of fields. The underlying goal is to identify the impulse response…
Under standard graphical assumptions, the Markov boundary of a target variable is the smallest set of features that renders every other feature redundant. Once the boundary is observed, the target is conditionally independent of the rest of…
A matrix is $k$-nonnegative if all its minors of size $k$ or less are nonnegative. We give a parametrized set of generators and relations for the semigroup of $k$-nonnegative $n\times n$ invertible matrices in two special cases: when $k =…