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This paper focuses on the analysis of real-time non preemptive multiprocessor scheduling with precedence and several latency constraints. It aims to specify a schedulability condition which enables a designer to check a priori -without…
We derive an integration by parts formula for functionals of determinantal processes on compact sets, completing the arguments of [4]. This is used to show the existence of a configuration-valued diffusion process which is non-colliding and…
Understanding posterior contraction behavior in Bayesian hierarchical models is of fundamental importance, but progress in this question is relatively sparse in comparison to the theory of density estimation. In this paper, we study two…
Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over…
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…
Multilayer networks are the underlying structures of multiple real-world systems where we have more than one type of interaction/relation between nodes: social, biological, computer, or communication, to name only a few. In many cases, they…
One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…
Recently in the field of unsupervised representation learning, strong identifiability results for disentanglement of causally-related latent variables have been established by exploiting certain side information, such as class labels, in…
Biclustering is a class of techniques that simultaneously clusters the rows and columns of a matrix to sort heterogeneous data into homogeneous blocks. Although many algorithms have been proposed to find biclusters, existing methods suffer…
A Bayesian belief network is a model of a joint distribution over a finite set of variables, with a DAG structure representing immediate dependencies among the variables. For each node, a table of parameters (CPtable) represents local…
We consider the problem of sequential learning from categorical observations bounded in [0,1]. We establish an ordering between the Dirichlet posterior over categorical outcomes and a Gaussian posterior under observations with N(0,1) noise.…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they…
Dynamical behaviors of complex interacting systems, including brain activities, financial price movements, and physical collective phenomena, are associated with underlying interactions between the system's components. The issue of…
Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems.…
A new approach on the joint estimation of partially exchangeable observations is presented by constructing pairwise dependence between $m$ random density functions, each of which is modeled as a mixture of geometric stick breaking…
We propose Derivative Learning (DERL), a supervised approach that models physical systems by learning their partial derivatives. We also leverage DERL to build physical models incrementally, by designing a distillation protocol that…