Seminar overview

Functional genomics has a long tradition of inferring the inner working of a cell through analysis of its response to various perturbations. Observing cellular features after knocking out or silencing a gene reveals which genes are essential for an organism or for a particular pathway. A key obstacle to inferring genetic networks from perturbation screens is that phenotypic profiles generally offer only indirect information on how genes interact. I will discuss a network inference method that we called Nested Effects Models (NEM). It can be used to model the flow of information in cells based on the nested structure of downstream effects of perturbations like RNAi mediated gene knockdowns. Special attention will be given to strategies for controlling network complexity. I will demonstrate the power of our method in the context of modelling disrupted Wnt signalling in colorectal cancers.

There has been an explosion of statistical techniques labeled "causal inference methods," in which the statistical analysis model is at least partly derived from a formal causal model. Discussions of these methods may leave the impression that they solve a unique and general problem of causal inference. That is not the case: Formal causal inference methods thus far focus on idealized special cases in which the only available evidence comprises one study or a set of similar studies, whereas there are usually diverse evidence sources that must be merged to form credible inferences. This reality is addressed by informal "criterion" or "checklist" approaches typified by Bradford Hill's nine causal considerations. Attempts to at least partially formalize causal considerations have as yet had limited contact with formal causal modeling, although those considerations can be formalized and merged with causal modeling to produce predictive theories of causal inference. Nonetheless, the effort required for integrative approaches combined with pressures to claim inferences from single evidence sources remain formidable obstacles to implementation of those approaches,

Outlines of a bayes-non-Bayes compromise or fusion have been emerging for decades. Nonetheless, basic teaching remains mired in conventional frequentist methods that are misunderstood and misrepresented by most users (including many statisticians) and that are highly misleading outside of ideal experimental conditions. Thus it is essential to revolutionize how we introduce elementary statistical inference in health and social science, by providing Bayesian concepts and methods in tandem with frequentist concepts and methods. Contrary to prevalent beliefs, basic Bayesian methods require no new computational formulas or software beyond familiar frequentist ones; they do not even require Bayes’ theorem. Those methods can help reveal untenably strong assumptions hidden in conventional methods, and allow relaxation of those assumptions into a more reasonable form. Background cite: Greenland, S. (2009). Relaxation penalties and priors for plausible modeling of non identified bias sources. Statistical Science, 24, 195-210

In recent years network analysis have become the focus of much research in many fields including biology, communication studies, economics, information science, organizational studies, and social psychology. Communities or clusters of highly connected actors form an essential feature in the structure of several empirical networks. Spectral clustering is a popular and computationally feasible method to discover these communities. The Stochastic Block Model is a social network model with well defined communities. This talk will give conditions for spectral clustering to correctly estimate the community membership of nearly all nodes. These asymptotic results are the first clustering results that allow the number of clusters in the model to grow with the number of nodes, hence the name high-dimensional. Moreover, I will present on-going work on directed spectral clustering for networks whose edges are directed, including the enron data as an example.

Factor model methods recently have become extremely popular in the theory and practice of large panels of time series data. Those methods rely on various models which all are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni, Hallin, Lippi and Reichlin (2000). In that paper, however, estimation relies on Brillinger's concept of dynamic principal components, which produces filters that are in general two-sided and therefore yield poor performances at the end of the observation period and hardly can be used for prediction purposes. In this talk, we show how to remedy this problem, and how, based on recent results on singular stationary processes with rational spectra, one-sided estimators can be constructed for the parameters and the common shocks in the GDFM. Consistency is obtained, along with rates. An empirical example, based on US macroeconomic time series, compares estimates based on our model with those based on the usual static-representation restriction, and provides convincing evidence that the assumptions underlying the latter are not supported by the data.

Pair-copula constructions (PCCs) allow to build very flexible multivariate statistical models based on a graphical representation called a regular vine (Kurowicka and Cooke, 2006) as well as models represented by directed acyclic graphs (DAGs). PCCs are very useful for modeling multivariate data in economics and finance, since they can capture non-symmetric and different tail dependences for different pairs of variables separately. Vine models are characterized by a sequence of linked trees called a vine-tree structure, bivariate copula families and families of marginal distributions. Two often studied subclasses are C- and D-vines. The multivariate normal and t distribution families are special cases. Moreover, PCCs can be used to construct non-Gaussian DAG models. First, research was focused on the development of efficient estimation methods. For regular vine models see for example Aas et. al. (2009) for likelihood based and Min and Czado (2010) for Bayesian estimation methods. For non-Gaussian DAGs model formulation and estimation methods are considered in Bauer et. al. (2012). Since the class of regular vine models is very large, model selection is vital. Dissmann et. al. (2011) provide a fast selection method in which trees are sampled sequentially using algorithms for weighted graphs. Bayesian alternatives are available. For non-Gaussian DAGs the model selection involves also a data-based selection of the DAG. We provide an alternative approach to the PC algorithm (Spirtes et. al., 2001) based on regular vines to allow for the detection of non-Gaussian dependency structures and compare its performance to the benchmark PC algorithm based on an independence test for zero partial correlation. We will discuss these PCC models and the associated selection methods as well illustrate them in an application to daily stock returns.

The talk is on the basic problem of estimating, from observed data, a probabilistic model which is parameterized by a finite number of parameters. Focus of the talk is on the particular situation where the model probability density function is unnormalized. That is, the model will not integrate to one for all values of the parameters. Maximum likelihood estimation can then not be used without resorting to numerical approximations which are often computationally expensive. In the talk, I will first give some background on unnormalized models. Then, I will introduce you to a novel method to estimate them, explain some of its properties, and show how it is used in the modeling of images. The talk is based on the following publication: Michael U. Gutmann and Aapo Hyvärinen, Noise-Contrastive Estimation of Unnormalized Statistical Models, with Applications to Natural Image Statistics, Journal of Machine Learning Research, 13(Feb):307−361, 2012. http://jmlr.csail.mit.edu/papers/v13/gutmann12a.html

In this talk I will present a new framework for deriving prior distributions in nonlinear dose-response modelling situations. Determination of the prior in these situations is challenging, as traditional approaches for prior selection in the case of little prior information (such as Jeffreys prior) are not adequate, which lead practitioners to choose prior distributions based on a mix of heuristic considerations and extensive simulations. In addition in pharmaceutical dose-response type trials the data are typically sparse, with a relatively small signal to noise ratio, which means that the prior will have a non- negligible influence on the posterior, which makes the choice of the prior even as more important. The essential idea of our approach is to derive the distribution in a way so that it is uniform in the underlying functional shapes of the nonlinear regression function, giving equal weight to all underlying shapes. We investigate the resulting unference procedure in two pharmaceutical clinical trial examples, and provide practical hints on how to implement the presented priors in Bayesian modelling software.

In this talk I will consider an application in Astronomy and illustrate how statistical procedures can be used to answer the important scientific questions. Whether a dwarf spheroidal galaxy is in equilibrium or being tidally disrupted by the Milky Way is an important question for the study of its dark matter content and distribution. This question is investigated using observations from the dwarf spheroidal Leo I. For Leo I, tidal disruption is detected, at least for stars sufficiently far from the centre, but the effect appears to be quite modest.

The talk will introduce nonparametric function estimation under known shape constraints. In the first part of the talk, I focus on construction of confidence intervals (CIs) for an unknown non-increasing density function on the positive real line based on the Grenander estimator, the nonparametric maximum likelihood estimator. This estimator, a prototypical example of a class of shape constrained estimators in one dimension, converges at rate cube-root n to a non-normal limit distribution. I investigate the consistency and performance of different bootstrap schemes for constructing point-wise CIs in this setup. In the second part of the talk I consider the nonparametric least squares estimation of a convex regression function when the dimension of the covariate can be greater than one. I characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs. I prove that under mild regularity conditions the estimator and its subdiff-erentials are consistent in both fixed and stochastic design regression settings.

Algorithms for inferring causality are heavily based on the Faithfulness assumption. The unfaithful distributions have measure zero and can be seen as a collection of hypersurfaces in a hypercube. The Faithfulness condition alone is not sufficient to guarantee uniform consistency and Strong-Faithfulness has been proposed to overcome this problem. In contrast to the original Faithfulness assumption, the set of distributions satisfying Strong-Faithfulness does not have measure one. We study the (Strong) Faithfulness condition from the point of view of real algebraic geometry and give upper and lower bounds on the proportion of unfaithful distributions for various classes of graphs.

We consider the problem of actively learning multi-index functions of the form f(x) = g(Ax)= \sum_{i=1}^k g_i(a_i^Tx) from point evaluations of f. We assume that the function f is defined on an l2-ball in R^d, g is twice continuously differentiable almost everywhere, and A \in {R}^{k \times d} is a rank k matrix, where k << d. We propose a randomized, active sampling scheme for estimating such functions with uniform approximation guarantees. Our theoretical developments leverage recent techniques from low rank matrix recovery, which enables us to derive an estimator of the function f along with sample complexity bounds. We also characterize the noise robustness of the scheme, and provide empirical evidence that the high-dimensional scaling of our sample complexity bounds is quite accurate.

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In this series of lectures we will first introduce the potential outcome approach to causal models. We will then introduce multivariate statistical models based on Directed Acyclic Graphs (DAGs), reviewing their basic Markov properties. We will then provide a causal interpretation for DAGs in terms of potential outcomes, relating this to the back-door formula and more generally, the do-calculus of Pearl. We will then consider two problems that arise in the context of a DAG model when we only observe a marginal distribution. First we consider the non-parametric dentification of causal effects, and describe a simple complete algorithm for this problem. Second, we will describe a general class of non-parametric constraints that are implied to hold in the observed marginal distribution, which we call the nested Markov property. We will describe parameterizations of some of the related statistical models. Finally, time permitting, we will describe approaches that have been proposed for dropping the assumption of acyclicity, describing some of the practical and theoretical obstacles. Prerequisites: Some basic familiarity with statistical problems.

In this series of lectures we will first introduce the potential outcome approach to causal models. We will then introduce multivariate statistical models based on Directed Acyclic Graphs (DAGs), reviewing their basic Markov properties. We will then provide a causal interpretation for DAGs in terms of potential outcomes, relating this to the back-door formula and more generally, the do-calculus of Pearl. We will then consider two problems that arise in the context of a DAG model when we only observe a marginal distribution. First we consider the non-parametric dentification of causal effects, and describe a simple complete algorithm for this problem. Second, we will describe a general class of non-parametric constraints that are implied to hold in the observed marginal distribution, which we call the nested Markov property. We will describe parameterizations of some of the related statistical models. Finally, time permitting, we will describe approaches that have been proposed for dropping the assumption of acyclicity, describing some of the practical and theoretical obstacles. Prerequisites: Some basic familiarity with statistical problems.

Photon-limited imaging, which arises in applications such as spectral imaging, night vision, nuclear medicine and astronomy, occurs when the number of photons collected by a sensor is small relative to the desired image resolution. Typically a Poisson distribution is used to model these observations, and the inherent heteroscedasticity of the data combined with standard noise removal methods yields significant artifacts. This paper introduces a novel denoising algorithm for photon-limited images which combines elements of dictionary learning and sparse epresentations for image patches. The method employs both an adaptation of Principal Component Analysis (PCA) for Poisson noise. A comprehensive empirical evaluation of the performance of the proposed method helps characterize the performance of this approach in very low light regimes relative to other state-of-the-art denoising methods. The results reveal that, despite its implicity, PCA-flavored denoising appears to be highly competitive in the presence of significant Poisson noise.

In this series of lectures we will first introduce the potential outcome approach to causal models. We will then introduce multivariate statistical models based on Directed Acyclic Graphs (DAGs), reviewing their basic Markov properties. We will then provide a causal interpretation for DAGs in terms of potential outcomes, relating this to the back-door formula and more generally, the do-calculus of Pearl. We will then consider two problems that arise in the context of a DAG model when we only observe a marginal distribution. First we consider the non-parametric dentification of causal effects, and describe a simple complete algorithm for this problem. Second, we will describe a general class of non-parametric constraints that are implied to hold in the observed marginal distribution, which we call the nested Markov property. We will describe parameterizations of some of the related statistical models. Finally, time permitting, we will describe approaches that have been proposed for dropping the assumption of acyclicity, describing some of the practical and theoretical obstacles. Prerequisites: Some basic familiarity with statistical problems.

In this series of lectures we will first introduce the potential outcome approach to causal models. We will then introduce multivariate statistical models based on Directed Acyclic Graphs (DAGs), reviewing their basic Markov properties. We will then provide a causal interpretation for DAGs in terms of potential outcomes, relating this to the back-door formula and more generally, the do-calculus of Pearl. We will then consider two problems that arise in the context of a DAG model when we only observe a marginal distribution. First we consider the non-parametric dentification of causal effects, and describe a simple complete algorithm for this problem. Second, we will describe a general class of non-parametric constraints that are implied to hold in the observed marginal distribution, which we call the nested Markov property. We will describe parameterizations of some of the related statistical models. Finally, time permitting, we will describe approaches that have been proposed for dropping the assumption of acyclicity, describing some of the practical and theoretical obstacles. Prerequisites: Some basic familiarity with statistical problems.