McGill Statistics Seminar

Date: 2020-10-09

Time: 15:30-16:30

Zoom Link

Meeting ID: 924 5390 4989

Passcode: 690084

Abstract:

Statistical learning theory is by now a mature branch of data science that hosts a vast variety of practical techniques for tackling data-related problems. In this talk we present some fundamental concepts upon which statistical learning theory has been based. Different approaches to statistical inference will be discussed and the main problem of learning from Vapnik’s point of view will be explained. Further we discuss the topic of function estimation as the heart of Vapnik-Chervonenkis theory. There exist several state-of-the-art methods for estimating functional dependencies, such as maximum margin estimator and artificial neural networks. While for some of these methods, e.g., the support vector machines, there has already been developed a profound theory, others require more investigation. Accordingly, we pay a closer attention to the so-called mapping neural networks and try to shed some light on certain theoretical aspects of them. We highlight some of the fundamental challenges that have attracted the attention of researcher and they are yet to be fully resolved. One of these challenges is estimation of the intrinsic dimension of data that will be discussed in detail. Another challenge is inferring causal direction when the training data set is not representative of the target population.

Date: 2020-09-25

Time: 14:00-15:00

Zoom Link

Meeting ID: 939 4707 7997

Passcode: no password

Abstract:

Network data is prevalent in many contemporary big data applications in which a common interest is to unveil important latent links between different pairs of nodes. Yet a simple fundamental question of how to precisely quantify the statistical uncertainty associated with the identification of latent links still remains largely unexplored. In this paper, we propose the method of statistical inference on membership profiles in large networks (SIMPLE) in the setting of degree-corrected mixed membership model, where the null hypothesis assumes that the pair of nodes share the same profile of community memberships. In the simpler case of no degree heterogeneity, the model reduces to the mixed membership model for which an alternative more robust test is also proposed. Both tests are of the Hotelling-type statistics based on the rows of empirical eigenvectors or their ratios, whose asymptotic covariance matrices are very challenging to derive and estimate. Nevertheless, their analytical expressions are unveiled and the unknown covariance matrices are consistently estimated. Under some mild regularity conditions, we establish the exact limiting distributions of the two forms of SIMPLE test statistics under the null hypothesis and contiguous alternative hypothesis. They are the chi-square distributions and the noncentral chi-square distributions, respectively, with degrees of freedom depending on whether the degrees are corrected or not. We also address the important issue of estimating the unknown number of communities and establish the asymptotic properties of the associated test statistics. The advantages and practical utility of our new procedures in terms of both size and power are demonstrated through several simulation examples and real network applications.

Date: 2020-09-18

Time: 15:30-16:30

Zoom Link

Meeting ID: 924 5390 4989

Passcode: 690084

Abstract:

With advances in mathematical modeling and computational methods, complex phenomena (e.g., universe formations, rocket propulsion) can now be reliably simulated via computer code. This code solves a complicated system of equations representing the underlying science of the problem. Such simulations can be very time-intensive, requiring months of computation for a single run. Gaussian processes (GPs) are widely used as predictive models for “emulating” this expensive computer code. Yet with limited training data on a high-dimensional parameter space, such models can suffer from poor predictive performance and physical interpretability. Fortunately, in many physical applications, there is additional boundary information on the code beforehand, either from governing physics or scientific knowledge. We propose a new BdryGP model which incorporates such boundary information for prediction. We show that BdryGP not only enjoys improved convergence rates over standard GP models which do not incorporate boundaries, but is also more resistant to the ``curse-of-dimensionality’’ in nonparametric regression. We then demonstrate the improved predictive performance and posterior contraction of the BdryGP model on several test problems in the literature.

Date: 2020-03-27

Time: 15:30-16:30

Location: BURNSIDE 1205

Abstract:

Generalized structured component analysis (GSCA) was developed as a component-based approach to structural equation modeling, where constructs are represented by components or weighted composites of observed variables, rather than (common) factors. Unlike another long-lasting component-based approach – partial least squares path modeling, GSCA is a full-information method that optimizes a single criterion to estimate model parameters simultaneously, utilizing all information available in the entire system of equations. Over the decade, this approach has been refined and extended in various ways to enhance its data-analytic capability. I will briefly discuss the theoretical underpinnings of GSCA and demonstrate the use of an R package for GSCA - gesca. Moreover, I will outline some recent developments in GSCA, which include GSCA_M for estimating models with factors and integrated GSCA (IGSCA) for estimating models with both factors and components.

Date: 2020-03-20

Time: 15:30-16:30

Location: BURNSIDE 1205

Abstract:

Historical data from previous studies may be utilized to strengthen statistical inference. Under the Bayesian framework incorporation of information obtained from any source other than the current data is facilitated through construction of an informative prior. The existing methodology for defining an informative prior based on historical data relies on measuring similarity to the current data at the study level that can result in discarding useful individual patient data (IPD). In this talk I present a family of priors that utilize IPD to strengthen statistical inference. IPD-based priors can be obtained as a weighted likelihood of the historical data where each individual’s weight is a function of their distance to the current study population. It is demonstrated that the proposed prior construction approach can considerably improve estimation accuracy and precision in compare with existing methods.

Date: 2020-03-13

Time: 15:30-16:30

Location: BURNSIDE 1205

Abstract:

High-throughput data collection technologies are becoming increasingly common in many fields, especially in biomedical applications involving single cell data (e.g., scRNA-seq and CyTOF). These introduce a rising need for exploratory analysis to reveal and understand hidden structure in the collected (high-dimensional) Big Data. A crucial aspect in such analysis is the separation of intrinsic data geometry from data distribution, as (a) the latter is typically biased by collection artifacts and data availability, and (b) rare subpopulations and sparse transitions between meta-stable states are often of great interest in biomedical data analysis. In this talk, I will show several tools that leverage manifold learning, graph signal processing, and harmonic analysis for biomedical (in particular, genomic/proteomic) data exploration, with emphasis on visualization, data generation/augmentation, and nonlinear feature extraction. A common thread in the presented tools is the construction of a data-driven diffusion geometry that both captures intrinsic structure in data and provides a generalization of Fourier harmonics on it. These, in turn, are used to process data features along the data geometry for denoising and generative purposes. Finally, I will relate this approach to the recently-proposed geometric scattering transform that generalizes Mallat’s scattering to non-Euclidean domains, and provides a mathematical framework for theoretical understanding of the emerging field of geometric deep learning.

Date: 2020-02-21

Time: 15:30-16:30

Location: BURNSIDE 1205

Abstract:

The goal of this presentation is to introduce new families of multivariate copulas, extending the chi-square copulas, the Fisher copula, and squared copulas. The new families are constructed from existing copulas by first transforming their margins to standard Gaussian distributions, then transforming these variables into non-central chi-square variables with one degree of freedom, and finally by considering the copula associated with these new variables. It is shown that by varying the non-centrality parameters, one can model non-monotonic dependence, and when one or many non-centrality parameters are outside a given hyper-rectangle, then the copula is almost the same as the one when these parameters are infinite. For these new families, the tail behavior, the monotonicity of dependence measures such as Kendall’s tau and Spearman’s rho are investigated, and estimation is discussed. Some examples will illustrate the usefulness of these new copula families.

Date: 2020-02-14

Time: 15:30-16:30

Location: BURNSIDE 1205

Abstract:

Many cities worldwide are embracing electric vehicle (EV) sharing as a flexible and sustainable means of urban transit. However, it remains challenging for the operators to charge the fleet due to limited or costly access to charging facilities. In this work, we focus on answering the core question - how to charge the fleet to make EV sharing viable and profitable. Our work is motivated by the recent setback that struck San Diego, California, where car2go ceased its EV sharing operations. We integrate charging infrastructure planning and vehicle repositioning operations that were often considered separately in the literature. More interestingly, our modeling emphasizes the operator-controlled charging operations and customers’ EV picking behavior, which are both central to EV sharing but were largely overlooked. Motivated by the actual data of car2go, our model explicitly characterizes how customers endogenously pick EVs based on energy levels, and how the operator dispatches EV charging under a targeted charging policy. We formulate the integrated model as a nonlinear optimization program with fractional constraints. We then develop both lower- and upper-bound formulations as mixed-integer second order cone programs, which are computationally tractable with small optimality gap. Contrary to car2go’s practice, we find that the viability of EV sharing can be enhanced by concentrating limited charger resources at selected locations. Charging EVs in a proactive fashion (rather than car2go’s policy of charging EVs only when their energy level drops below 20%) can boost the profit by 10.7%. Given the demand profile in San Diego, the fleet size may reduce by up to 34% without incurring significant profit loss. Moreover, sufficient charger availability is crucial when collaborating with a public charger network. Finally, increasing the charging power relieves the charger resource constraint, whereas extending per-charge range or adopting unmanned repositioning improves profitability. In summary, our work demonstrates a data-verified and high-granularity modeling approach. Both the high-level planning guidelines and operational policies can be useful for practitioners. We also highlight the value of jointly managing demand fulfilment and EV charging.

Date: 2020-01-31

Time: 15:30-16:30

Location: BURNSIDE 1104

Abstract:

I’ll discuss the use of observational data to estimate the causal effect of a treatment on an outcome. This task is complicated by the presence of “confounders” that influence both treatment and outcome, inducing observed associations that are not causal. Causal estimation is achieved by adjusting for this confounding by using observed covariate information. I’ll discuss the case where we observe covariates that carry sufficient information for the adjustment. But where explicit models relating treatment, outcome, covariates and confounding are not available.

Date: 2020-01-13

Time: 15:30-16:30

Location: BURNSIDE 1205

Abstract:

This talk is motivated by statistical challenges that arise in the analysis of calcium imaging data, a new technology in neuroscience that makes it possible to record from huge numbers of neurons at single-neuron resolution. In the first part of this talk, I will consider the problem of estimating a neuron’s spike times from calcium imaging data. A simple and natural model suggests a non-convex optimization problem for this task. I will show that by recasting the non-convex problem as a changepoint detection problem, we can efficiently solve it for the global optimum using a clever dynamic programming strategy.