/categories/mcgill-statistics-seminar/index.xml McGill Statistics Seminar - McGill Statistics Seminars

McGill Statistics Seminar

  • A fast unified algorithm for solving group Lasso penalized learning problems

    Yi Yang · Feb 5, 2015

    Date: 2015-02-05

    Time: 15:30-16:30

    Location: BURN 1B39

    Abstract:

    We consider a class of group-lasso learning problems where the objective function is the sum of an empirical loss and the group-lasso penalty. For a class of loss function satisfying a quadratic majorization condition, we derive a unified algorithm called groupwise-majorization-descent (GMD) for efficiently computing the solution paths of the corresponding group-lasso penalized learning problem. GMD allows for general design matrices, without requiring the predictors to be group-wise orthonormal. As illustration examples, we develop concrete algorithms for solving the group-lasso penalized least squares and several group-lasso penalized large margin classifiers. These group-lasso models have been implemented in an R package gglasso publicly available from the Comprehensive R Archive Network (CRAN) at http://cran.r-project.org/web/packages/gglasso. On simulated and real data, gglasso consistently outperforms the existing software for computing the group-lasso that implements either the classical groupwise descent algorithm or Nesterov’s method. An application in risk segmentation of insurance business is illustrated by analysis of an auto insurance claim dataset.

  • Joint analysis of multiple multi-state processes via copulas

    Liqun Diao · Feb 2, 2015

    Date: 2015-02-02

    Time: 15:30-16:30

    Location: BURN 1214

    Abstract:

    A copula-based model is described which enables joint analysis of multiple progressive multi-state processes. Unlike intensity-based or frailty-based approaches to joint modeling, the copula formulation proposed herein ensures that a wide range of marginal multi-state processes can be specified and the joint model will retain these marginal features. The copula formulation also facilitates a variety of approaches to estimation and inference including composite likelihood and two-stage estimation procedures. We consider processes with Markov margins in detail, which are often suitable when chronic diseases are progressive in nature. We give special attention to the setting in which individuals are examined intermittently and transition times are consequently interval-censored. Simulation studies give empirical insight into the different methods of analysis and an application involving progression in joint damage in psoriatic arthritis provides further illustration.

  • Distributed estimation and inference for sparse regression

    Yuekai Sun · Jan 30, 2015

    Date: 2015-01-30

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    We address two outstanding challenges in sparse regression: (i) computationally efficient estimation in distributed settings; (ii) valid inference for the selected coefficients. The main computational challenge in a distributed setting is harnessing the computational capabilities of all the machines while keeping communication costs low. We devise an approach that requires only a single round of communication among the machines. We show the approach recovers the convergence rate of the (centralized) lasso as long as each machine has access to an adequate number of samples. Turning to the second challenge, we devise an approach to post-selection inference by conditioning on the selected model. In a nutshell, our approach gives inferences with the same frequency interpretation as those given by data/sample splitting, but it is more broadly applicable and more powerful. The validity of our approach also does not depend on the correctness of the selected model, i.e., it gives valid inferences even when the selected model is incorrect.

  • Simultaneous white noise models and shrinkage recovery of functional data

    Fang Yao · Jan 16, 2015

    Date: 2015-01-16

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    We consider the white noise representation of functional data taken as i.i.d. realizations of a Gaussian process. The main idea is to establish an asymptotic equivalence in Le Cam’s sense between an experiment which simultaneously describes these realizations and a collection of white noise models. In this context, we project onto an arbitrary basis and apply a novel variant of Stein-type estimation for optimal recovery of the realized trajectories. A key inequality is derived showing that the corresponding risks, conditioned on the underlying curves, are minimax optimal and can be made arbitrarily close to those that an oracle with knowledge of the process would attain. Empirical performance is illustrated through simulated and real data examples.

  • Mixtures of coalesced generalized hyperbolic distributions

    Ryan P. Browne · Jan 13, 2015

    Date: 2015-01-13

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    A mixture of coalesced generalized hyperbolic distributions is developed by joining a finite mixture of generalized hyperbolic distributions with a mixture of multiple scaled generalized hyperbolic distributions. The result is a mixture of mixtures with shared model parameters and common mode. We begin by discussing the generalized hyperbolic distribution, which has the t, Gaussian and others as special cases. The generalized hyperbolic distribution can represented as a normal-variance mixture using a generalized inverse Gaussian distribution. This representation makes it a suitable candidate for the expectation-maximization algorithm. Secondly, we discuss the multiple scale generalized hyperbolic distribution which arises via implementation of a multi-dimensional weight function. A parameter estimation scheme is developed using the ever-expanding class of MM algorithms and the Bayesian information criterion is used for model selection. Special consideration is given to the contour shape. We use the coalesced distribution for clustering and compare them to finite mixtures of skew-t distributions using simulated and real data sets. Finally, the role of generalized hyperbolic mixtures within the wider model-based clustering, classification, and density estimation literature is discussed.

  • Space-time data analysis: Out of the Hilbert box

    James O. Ramsay · Jan 9, 2015

    Date: 2015-01-09

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Given the discouraging state of current efforts to curb global warming, we can imagine that we will soon turn our attention to mitigation. On a global scale, distressed populations will turn to national and international organizations for solutions to dramatic problems caused by climate change. These institutions in turn will mandate the collection of data on a scale and resolution that will present extraordinary statistical and computational challenges to those of us viewed as having the appropriate expertise. A review of the current state of our space-time data analysis machinery suggests that we have much to do. Most of current spatial modelling methodology is based on concepts translated from time series analysis, is heavily dependent on various kinds of stationarity assumptions, uses the Gaussian distribution to model data and depends on a priori coordinate systems that do not exist in nature. A way forward from this restrictive framework is proposed by modelling data over textured domains using layered coordinate systems.

  • Testing for structured Normal means

    James Sharpnack · Dec 12, 2014

    Date: 2014-12-12

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    We will discuss the detection of pattern in images and graphs from a high-dimensional Gaussian measurement. This problem is relevant to many applications including detecting anomalies in sensor and computer networks, large-scale surveillance, co-expressions in gene networks, disease outbreaks, etc. Beyond its wide applicability, structured Normal means detection serves as a case study in the difficulty of balancing computational complexity with statistical power. We will begin by discussing the detection of active rectangles in images and sensor grids. We will develop an adaptive scan test and determine its asymptotic distribution. We propose an approximate algorithm that runs in nearly linear time but achieves the same asymptotic distribution as the naive, quadratic run-time algorithm. We will move on to the more general problem of detecting a well-connected active subgraph within a graph in the Normal means context. Because the generalized likelihood ratio test is computationally infeasible, we propose approximate algorithms and study their statistical efficiency. One such algorithm that we develop is the graph Fourier scan statistic, whose statistical performance is characterized by the spectrum of the graph Laplacian. Another relaxation that we have developed is the Lovasz extended scan statistic (LESS), which is based on submodular optimization and the performance is described using electrical network theory. We also introduce the spanning tree wavelet basis over graphs, a localized basis that reflects the topology of the graph. For each of these tests we compare their statistical guarantees to an information theoretic lower bound.

  • Copula model selection: A statistical approach

    Julien Roger · Dec 5, 2014

    Date: 2014-12-05

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Copula model selection is an important problem because similar but differing copula models can offer different conclusions surrounding the dependence structure of random variables. Chen & Fan (2005) proposed a model selection method involving a statistical hypothesis test. The hypothesis test attempts to take into account the randomness of the AIC and other likelihood-based model selection methods for finite samples. Performance of the test compared to the more common approach of AIC is illustrated in a series of simulations.

  • Model-based methods of classification with applications

    Irene Vrbik · Nov 28, 2014

    Date: 2014-11-28

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Model-based clustering via finite mixture models is a popular clustering method for finding hidden structures in data. The model is often assumed to be a finite mixture of multivariate normal distributions; however, flexible extensions have been developed over recent years. This talk demonstrates some methods employed in unsupervised, semi-supervised, and supervised classification that include skew-normal and skew-t mixture models. Both real and simulated data sets are used to demonstrate the efficacy of these techniques.

  • Estimating by solving nonconvex programs: Statistical and computational guarantees

    Martin J. Wainwright · Nov 21, 2014

    Date: 2014-11-21

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Many statistical estimators are based on solving nonconvex programs. Although the practical performance of such methods is often excellent, the associated theory is frequently incomplete, due to the potential gaps between global and local optima. In this talk, we present theoretical results that apply to all local optima of various regularized M-estimators, where both loss and penalty functions are allowed to be nonconvex. Our theory covers a broad class of nonconvex objective functions, including corrected versions of the Lasso for error-in-variables linear models; regression in generalized linear models using nonconvex regularizers such as SCAD and MCP; and graph and inverse covariance matrix estimation. Under suitable regularity conditions, our theory guarantees that any local optimum of the composite objective function lies within statistical precision of the true parameter vector. This result closes the gap between theory and practice for these methods.