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Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…
Financial studies require volatility based models which provides useful insights on risks related to investments. Stochastic volatility models are one of the most popular approaches to model volatility in such studies. The asset returns…
In this contribution we deal with the problem of learning an undirected graph which encodes the conditional dependence relationship between variables of a complex system, given a set of observations of this system. This is a very central…
We develop a class of nearest-neighbor mixture models that provide direct, computationally efficient, probabilistic modeling for non-Gaussian geospatial data. The class is defined over a directed acyclic graph, which implies conditional…
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…
This paper presents an approach that brings together game theory with grammatical inference and discrete abstractions in order to synthesize control strategies for hybrid dynamical systems performing tasks in partially unknown but…
A method is presented for the rhythmic parsing problem: Given a sequence of observed musical note onset times, we estimate the corresponding notated rhythm and tempo process. A graphical model is developed that represents the simultaneous…
Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data.…
We consider the simulation of distributions that are a mixture of discrete and continuous components. We extend a Metropolis-Hastings-based perfect sampling algorithm of Corcoran and Tweedie to allow for a broader class of transition…
We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the…
An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of…
Considering discrete models, the univariate framework has been studied in depth compared to the multivariate one. This paper first proposes two criteria to define a sensu stricto multivariate discrete distribution. It then introduces the…
We present a Bayesian model for estimating the joint distribution of multivariate categorical data when units are nested within groups. Such data arise frequently in social science settings, for example, people living in households. The…
We consider the stability and the input-output analysis problems of a class of large-scale hybrid systems composed of continuous dynamics coupled with discrete dynamics defined over finite alphabets, e.g., deterministic finite state…
We propose a new modeling approach that is a generalization of generative and discriminative models. The core idea is to use an implicit parameterization of a joint probability distribution by specifying only the conditional distributions.…
Neural networks and other machine learning models compute continuous representations, while humans communicate mostly through discrete symbols. Reconciling these two forms of communication is desirable for generating human-readable…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
A continuous approximation framework for non-linear stochastic as well as deterministic discrete maps is developed. For the stochastic map with uncorelated Gaussian noise, by successively applying the It\^o lemma, we obtain a Langevin type…
Multivariate count data are defined as the number of items of different categories issued from sampling within a population, which individuals are grouped into categories. The analysis of multivariate count data is a recurrent and crucial…
We introduce the Graph Mixture Density Networks, a new family of machine learning models that can fit multimodal output distributions conditioned on graphs of arbitrary topology. By combining ideas from mixture models and graph…