/tags/2019-winter/index.xml 2019 Winter - McGill Statistics Seminars

2019 Winter

  • Network models, sampling, and symmetry properties

    Peter Orbanz · Feb 1, 2019

    Date: 2019-02-01

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    A recent body of work, by myself and many others, aims to develop a statistical theory of network data for problems a single network is observed. Of the models studied in this area, graphon models are probably most widely known in statistics. I will explain the relationship between three aspects of this work: (1) Specific models, such as graphon models, graphex models, and edge-exchangeable graphs. (2) Sampling theory for networks, specifically in the case statisticians might refer to as an infinite-population limit. (3) Invariance properties, especially various forms of exchangeability. I will also present recent results that show how statistically relevant results (such as central limit theorems) can be derived from such invariance properties.

  • Modern Non-Problems in Optimization: Applications to Statistics and Machine Learning

    Ying Cui · Jan 25, 2019

    Date: 2019-01-25

    Time: 16:00-17:00

    Location: BURN 920

    Abstract:

    We have witnessed a lot of exciting development of data science in recent years. From the perspective of optimization, many modern data-science problems involve some basic ``non’’-properties that lack systematic treatment by the current approaches for the sake of the computation convenience. These non-properties include the coupling of the non-convexity, non-differentiability and non-determinism. In this talk, we present rigorous computational methods for solving two typical non-problems: the piecewise linear regression and the feed-forward deep neural network. The algorithmic framework is an integration of the first order non-convex majorization-minimization method and the second order non-smooth Newton methods. Numerical experiments demonstrate the effectiveness of our proposed approach. Contrary to existing methods for solving non-problems which provide at best very weak guarantees on the computed solutions obtained in practical implementation, our rigorous mathematical treatment aims to understand properties of these computed solutions with reference to both the empirical and the population risk minimizations.

  • Singularities of the information matrix and longitudinal data with change points

    Masoud Asgharian · Jan 18, 2019

    Date: 2019-01-18

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Non-singularity of the information matrix plays a key role in model identification and the asymptotic theory of statistics. For many statistical models, however, this condition seems virtually impossible to verify. An example of such models is a class of mixture models associated with multi-path change-point problems (MCP) which can model longitudinal data with change points. The MCP models are similar in nature to mixture-of-experts models in machine learning. The question then arises as to how often the non-singularity assumption of the information matrix fails to hold. We show that

  • Magic Cross-Validation Theory for Large-Margin Classification

    Boxiang Wang · Jan 11, 2019

    Date: 2019-01-11

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Cross-validation (CV) is perhaps the most widely used tool for tuning supervised machine learning algorithms in order to achieve better generalization error rate. In this paper, we focus on leave-one-out cross-validation (LOOCV) for the support vector machine (SVM) and related algorithms. We first address two wide-spreading misconceptions on LOOCV. We show that LOOCV, ten-fold, and five-fold CV are actually well-matched in estimating the generalization error, and the computation speed of LOOCV is not necessarily slower than that of ten-fold and five-fold CV. We further present a magic CV theory with a surprisingly simple recipe which allows users to very efficiently tune the SVM. We then apply the magic CV theory to demonstrate a straightforward way to prove the Bayes risk consistency of the SVM. We have implemented our algorithms in a publicly available R package magicsvm, which is much faster than the state-of-the-art SVM solvers. We demonstrate our methods on extensive simulations and benchmark examples.