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

McGill Statistics Seminar

  • Automated Inference on Sharp Bounds

    Vira Semenova · Nov 11, 2022

    Date: 2022-11-11

    Time: 15:30-16:30 (Montreal time)

    https://mcgill.zoom.us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09

    Meeting ID: 834 3668 6293

    Passcode: 12345

    Abstract:

    Many causal parameters involving the joint distribution of potential outcomes in treated and control states cannot be point-identified, but only be bounded from above and below. The bounds can be further tightened by conditioning on pre-treatment covariates, and the sharp version of the bounds corresponds to using a full covariate vector. This paper gives a method for estimation and inference on sharp bounds determined by a linear system of under-identified equalities (e.g., as in Heckman et al (ReSTUD, 1997)). In the sharp bounds’ case, the RHS of this system involves a nuisance function of (many) covariates (e.g., the conditional probability of employment in treated or control state). Combining Neyman-orthogonality and sample splitting, I provide an asymptotically Gaussian estimator of sharp bound that does not require solving the linear system in closed form. I demonstrate the method in an empirical application to Connecticut’s Jobs First welfare reform experiment.

  • Max-linear Graphical Models for Extreme Risk Modelling

    Claudia Klüppelberg · Nov 4, 2022

    Date: 2022-11-04

    Time: 15:30-16:30 (Montreal time)

    https://mcgill.zoom.us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09

    Meeting ID: 834 3668 6293

    Passcode: 12345

    Abstract:

    Graphical models can represent multivariate distributions in an intuitive way and, hence, facilitate statistical analysis of high-dimensional data. Such models are usually modular so that high-dimensional distributions can be described and handled by careful combination of lower dimensional factors. Furthermore, graphs are natural data structures for algorithmic treatment. Moreover, graphical models can allow for causal interpretation, often provided through a recursive system on a directed acyclic graph (DAG) and the max-linear Bayesian network we introduced in [1] is a specific example. This talk contributes to the recently emerged topic of graphical models for extremes, in particular to max-linear Bayesian networks, which are max-linear graphical models on DAGs. Generalized MLEs are derived in [2]. In this context, the Latent River Problem has emerged as a flagship problem for causal discovery in extreme value statistics. In [3] we provide a simple and efficient algorithm QTree to solve the Latent River Problem. QTree returns a directed graph and achieves almost perfect recovery on the Upper Danube, the existing benchmark dataset, as well as on new data from the Lower Colorado River in Texas. It can handle missing data, and has an automated parameter tuning procedure. In our paper, we also show that, under a max-linear Bayesian network model for extreme values with propagating noise, the QTree algorithm returns asymptotically a.s. the correct tree. Here we use the fact that the non-noisy model has a left-sided atom for every bivariate marginal distribution, when there is a directed edge between the the nodes.

  • A Conformal-Based Two-Sample Conditional Distribution Test

    Jing Lei · Oct 21, 2022

    Date: 2022-10-21

    Time: 15:30-16:30 (Montreal time)

    https://mcgill.zoom.us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09

    Meeting ID: 834 3668 6293

    Passcode: 12345

    Abstract:

    We consider the problem of testing the equality of the conditional distribution of a response variable given a set of covariates between two populations. Such a testing problem is related to transfer learning and causal inference. We develop a nonparametric procedure by combining recent advances in conformal prediction with some new ingredients such as a novel choice of conformity score and data-driven choices of weight and score functions. To our knowledge, this is the first successful attempt of using conformal prediction for testing statistical hypotheses beyond exchangeability. The final test statistic reveals a natural connection between conformal inference and the classical rank-sum test. Our method is suitable for modern machine learning scenarios where the data has high dimensionality and the sample size is large, and can be effectively combined with existing classification algorithms to find good weight and score functions. The performance of the proposed method is demonstrated in synthetic and real data examples.

  • Some steps towards causal representation learning

    Jason Hartford · Oct 7, 2022

    Date: 2022-10-07

    Time: 15:30-16:30 (Montreal time)

    https://mcgill.zoom.us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09

    Meeting ID: 834 3668 6293

    Passcode: 12345

    Abstract:

    High-dimensional unstructured data such images or sensor data can often be collected cheaply in experiments, but is challenging to use in a causal inference pipeline without extensive engineering and domain knowledge to extract underlying latent factors. The long term goal of causal representation learning is to find appropriate assumptions and methods to disentangle latent variables and learn the causal mechanisms that explain a system’s behaviour. In this talk, I’ll present results from a series of recent papers that describe how we can leverage assumptions about a system’s causal mechanisms to provably disentangle latent factors. I will also talk about the limitations of a commonly used injectivity assumption, and discuss a hierarchy of settings that relax this assumption.

  • Statistical Inference for Functional Linear Quantile Regression

    Peijun Sang · Sep 16, 2022

    Date: 2022-09-16

    Time: 15:20-16:20 (Montreal time)

    https://mcgill.zoom.us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09

    Meeting ID: 834 3668 6293

    Passcode: 12345

    Abstract:

    We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ kernel convolution to smooth the original loss function. The coefficient function is estimated under a reproducing kernel Hilbert space framework. A gradient descent algorithm is designed to minimize the smoothed loss function with a roughness penalty. With the aid of the Banach fixed-point theorem, we show the existence and uniqueness of our proposed estimator as the minimizer of the regularized loss function in an appropriate Hilbert space. Furthermore, we establish the convergence rate as well as the weak convergence of our estimator. As far as we know, this is the first weak convergence result for a functional quantile regression model. Pointwise confidence intervals and a simultaneous confidence band for the true coefficient function are then developed based on these theoretical properties. Numerical studies including both simulations and a data application are conducted to investigate the performance of our estimator and inference tools in finite sample.

  • Markov-Switching State Space Models For Uncovering Musical Interpretation

    Daniel McDonald · Sep 9, 2022

    Date: 2022-09-09

    Time: 15:30-16:30 (Montreal time)

    https://mcgill.zoom.us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09

    Meeting ID: 834 3668 6293

    Passcode: 12345

    Abstract:

    For concertgoers, musical interpretation is the most important factor in determining whether or not we enjoy a classical performance. Every performance includes mistakes—intonation issues, a lost note, an unpleasant sound—but these are all easily forgotten (or unnoticed) when a performer engages her audience, imbuing a piece with novel emotional content beyond the vague instructions inscribed on the printed page. In this research, we use data from the CHARM Mazurka Project—forty-six professional recordings of Chopin’s Mazurka Op. 68 No. 3 by consummate artists—with the goal of elucidating musically interpretable performance decisions. We focus specifically on each performer’s use of musical tempo by examining the inter-onset intervals of the note attacks in the recording. To explain these tempo decisions, we develop a switching state space model and estimate it by maximum likelihood combined with prior information gained from music theory and performance practice. We use the estimated parameters to quantitatively describe individual performance decisions and compare recordings. These comparisons suggest methods for informing music instruction, discovering listening preferences, and analyzing performances.

  • Enriched post-selection models for high dimensional data

    Reza Drikvandi · Apr 8, 2022

    Date: 2022-04-08

    Time: 15:35-16:35 (Montreal time)

    https://mcgill.zoom.us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09

    Meeting ID: 834 3668 6293

    Passcode: 12345

    Abstract:

    High dimensional data are rapidly growing in many domains, for example, in microarray gene expression studies, fMRI data analysis, large-scale healthcare analytics, text/image analysis, natural language processing and astronomy, to name but a few. In the last two decades regularisation approaches have become the methods of choice for analysing high dimensional data. However, obtaining accurate estimates and predictions as well as valid statistical inference remains a major challenge in high dimensional situations. In this talk, we present enriched post-selection models that aim to improve parameter estimation and prediction, and to facilitate statistical inferences in high dimensional regression models. The enriched post-selection method enables us to construct valid post-selection inference for regression parameters in high dimensions. We discuss the empirical and asymptotic properties of the enriched post-selection method.

  • Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control

    Stephen Bates · Apr 1, 2022

    Date: 2022-04-01

    Time: 15:35-16:35 (Montreal time)

    https://mcgill.zoom.us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09

    Meeting ID: 834 3668 6293

    Passcode: 12345

    Abstract:

    We introduce Learn then Test, a framework for calibrating machine learning models so that their predictions satisfy explicit, finite-sample statistical guarantees regardless of the underlying model and (unknown) data-generating distribution. The framework addresses, among other examples, false discovery rate control in multi-label classification, intersection-over-union control in instance segmentation, and the simultaneous control of the type-1 error of outlier detection and confidence set coverage in classification or regression. To accomplish this, we solve a key technical challenge: the control of arbitrary risks that are not necessarily monotonic. Our main insight is to reframe the risk-control problem as multiple hypothesis testing, enabling techniques and mathematical arguments different from those in the previous literature. We use our framework to provide new calibration methods for several core machine learning tasks with detailed worked examples in computer vision.

  • Distribution-​free inference for regression: discrete, continuous, and in between

    Rina Foygel Barber · Mar 25, 2022

    Date: 2022-03-25

    Time: 15:35-16:35 (Montreal time)

    https://mcgill.zoom.us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09

    Meeting ID: 834 3668 6293

    Passcode: 12345

    Abstract:

    In data analysis problems where we are not able to rely on distributional assumptions, what types of inference guarantees can still be obtained? Many popular methods, such as holdout methods, cross-validation methods, and conformal prediction, are able to provide distribution-free guarantees for predictive inference, but the problem of providing inference for the underlying regression function (for example, inference on the conditional mean E[Y|X]) is more challenging. If X takes only a small number of possible values, then inference on E[Y|X] is trivial to achieve. At the other extreme, if the features X are continuously distributed, we show that any confidence interval for E[Y|X] must have non-vanishing width, even as sample size tends to infinity - this is true regardless of smoothness properties or other desirable features of the underlying distribution. In between these two extremes, we find several distinct regimes - in particular, it is possible for distribution-free confidence intervals to have vanishing width if and only if the effective support size of the distribution ofXis smaller than the square of the sample size.

  • New Approaches for Inference on Optimal Treatment Regimes

    Lan Wang · Mar 11, 2022

    Date: 2022-03-11

    Time: 15:30-16:30 (Montreal time)

    https://mcgill.zoom.us/j/83436686293?pwd=b0RmWmlXRXE3OWR6NlNIcWF5d0dJQT09

    Meeting ID: 834 3668 6293

    Passcode: 12345

    Abstract:

    Finding the optimal treatment regime (or a series of sequential treatment regimes) based on individual characteristics has important applications in precision medicine. We propose two new approaches to quantify uncertainty in optimal treatment regime estimation. First, we consider inference in the model-free setting, which does not require specifying an outcome regression model. Existing model-free estimators for optimal treatment regimes are usually not suitable for the purpose of inference, because they either have nonstandard asymptotic distributions or do not necessarily guarantee consistent estimation of the parameter indexing the Bayes rule due to the use of surrogate loss. We study a smoothed robust estimator that directly targets the parameter corresponding to the Bayes decision rule for optimal treatment regimes estimation. We verify that a resampling procedure provides asymptotically accurate inference for both the parameter indexing the optimal treatment regime and the optimal value function. Next, we consider the high-dimensional setting and propose a semiparametric model-assisted approach for simultaneous inference. Simulation results and real data examples are used for illustration.