2019 Fall

Date: 2019-11-29 Time: 15:30-16:30 Location: BURN 1205 Abstract: An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different diffusions are suitable for optimizing different classes of convex and non-convex functions. This allows us to design diffusions suitable for globally optimizing convex and non-convex functions not covered by the existing Langevin theory.

Date: 2019-11-22 Time: 16:00-17:00 Location: Pavillon Kennedy, PK-5115, UQAM Abstract: The stochastic inverse problem of determining probability structures on input parameters for a physics model corresponding to a given probability structure on the output of the model forms the core of scientific inference and engineering design. We describe a formulation and solution method for stochastic inverse problems that is based on functional analysis, differential geometry, and probability/measure theory. This approach yields a computationally tractable problem while avoiding alterations of the model like regularization and ad hoc assumptions about the probability structures.

Date: 2019-11-15 Time: 15:30-16:30 Location: BURN 1205 Abstract: Divergences, such as the Kullback-Leibler divergence, are distance-like quantities which arise in many applications in probability, statistics and data science. We introduce a family of logarithmic divergences which is a non-linear extension of the celebrated Bregman divergence. It is defined for any exponentially concave function (a function whose exponential is concave). We motivate this divergence by mathematical finance and large deviations of Dirichlet process.

Date: 2019-11-08 Time: 15:30-16:30 Location: BURN 1205 Abstract: Large scale multivariate regression with many heavy-tailed responses arises in a wide range of areas from genomics, financial asset pricing, banking regulation, to psychology and social studies. Simultaneously testing a large number of general linear hypotheses, such as multiple contrasts, based on the large scale multivariate regression reveals a variety of associations between responses and regression or experimental factors. Traditional multiple testing methods often ignore the effect of heavy-tailedness in the data and impose joint normality assumption that is arguably stringent in applications.

Date: 2019-11-01 Time: 16:00-17:00 Location: BURN 1104 Abstract: The work is motivated by the inflexibility of Bayesian modeling; in that only parameters of probability models are required to be connected with data. The idea is to generalize this by allowing arbitrary unknowns to be connected with data via loss functions. An updating process is then detailed which can be viewed as arising in at least a couple of ways - one being purely axiomatically driven.

Date: 2019-10-25 Time: 15:30-16:30 Location: BURN 1205 Abstract: High-dimensional point processes have become ubiquitous in many scientific fields. For instance, neuroscientists use calcium florescent imaging to monitor the firing of thousands of neurons in live animals. In this talk, I will discuss new methodological, computational and theoretical developments for learning neuronal connectivity networks from high-dimensional point processes. Time permitting, I will also discuss a new approach for handling non-stationarity in high-dimensional time series.

Date: 2019-10-18 Time: 15:30-16:30 Location: BURN 1205 Abstract: In its most common form extreme value theory is concerned with the limiting distribution of location-scale transformed block-maxima $M_n = \max(X_1,\dots,X_n)$ of a sequence of identically distributed random variables $(X_i)$, $i\geq 1$. In case the members of the sequence $(X_i)$ are independent, the weak limiting behaviour of $M_n$ is adequately described by the classical Fisher-Tippett-Gnedenko theorem. In this presentation we are interested in the case of dependent random variables $(X_i)$ while retaining a common marginal distribution function $F$ for all $X_i$, $i\in\mathbb{N}$.

Date: 2019-10-11 Time: 15:30-16:30 Location: BURN 1205 Abstract: Integral estimation in any dimension is an extensive topic, largely treated in the literature, with a broad range of applications. Monte-Carlo type methods arise naturally when one looks forward to quantifying/controlling the error. Many methods have already been developped: MCMC, Poisson disk sampling, QMC (and randomized versions), Bayesian quadrature, etc. In this talk, I’ll consider a different approach which consists in defining the quadrature nodes as the realization of a spatial point process.

Date: 2019-10-04 Time: 16:00-17:00 Location: CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 1355 Abstract: Modeling dependence between random variables is omnipresent in statistics. When rare events with high impact are involved, such as severe storms, floods or heat waves, the issue is both of great importance for risk management and theoretically challenging. Combining extreme-value theory with copula modeling and rank-based inference yields a particularly flexible and promising approach to this problem.

Date: 2019-09-27 Time: 15:30-16:30 Location: McIntyre Medical Building, Room 521 Abstract: This work is motivated by a problem in describing forest nitrogen cycling, and a consequent goal of constructing regression models for spatial images. Specifically, I present a functional concurrent linear model (FLCM) with varying coefficients for two-dimensional spatial images. To address overparameterization issues, the parameter surfaces in this model are transformed into the wavelet domain and then sparse representations are found using two different methods: LASSO and Bayesian variable selection.