糖心直播

Tisdag 6 oktober 15.15-17.00, Reza Arabi Belaghi (SLU)

Plats: BL34

Titel: Recent Advances in High-Dimensional Data Modeling: From Variable Selection and Machine Learning to Post-Selection Shrinkage and Statistical Inference

Sammanfattning: The rapid growth of high-dimensional data in genomics, biomedical research, environmental sciences, and other scientific disciplines has created statistical problems in which the number of potential predictors can be comparable to, or substantially larger than, the sample size. Although regularization methods such as LASSO and Elastic Net have transformed the analysis of such data, important challenges remain. In particular, variable selection can become unstable in the presence of highly correlated predictors, and procedures designed to produce sparse models may overlook predictors with weak but non-negligible signals. Consequently, selecting a sparse model is not necessarily the end of the statistical problem: how we estimate and make use of the information remaining after selection is equally important.

In this talk, I will discuss recent developments in high-dimensional statistical modeling from the complementary perspectives of variable selection, machine learning, and post-selection estimation. I will first examine the behaviour of classical penalized approaches such as LASSO and Elastic Net and contrast them with machine-learning-based screening methods such as Boruta. Particular attention will be given to the effects of dimensionality, predictor correlation, sample size, and signal strength on the ability of these methods to identify relevant variables.

I will then move from the question of which variables should be selected? to the equally important question of what should be done after selection? A central theme will be the distinction between strong, weak-to-moderate, and null signals. Rather than automatically discarding variables that fail to survive an initial sparse selection procedure, post-selection shrinkage methods can retain and appropriately down-weight information carried by weaker predictors. I will discuss recent extensions of this idea to high-dimensional generalized linear models and Cox proportional hazards models, including weighted-ridge and Stein-type shrinkage strategies designed to improve estimation and prediction in the presence of weak signals and multicollinearity.

Finally, I will discuss a broader 鈥渟creen鈥搕hen鈥搒hrink鈥� perspective that combines machine-learning screening with statistical shrinkage. Using high-dimensional beta regression as an example, I will illustrate how Boruta-based screening can first reduce an ultra-high-dimensional feature space,
after which ridge and Stein-type shrinkage can be used to stabilize estimation among correlated and potentially weak predictors. This provides a bridge between modern machine-learning feature discovery and classical statistical estimation and inference.

Throughout the talk, theoretical ideas will be connected with simulation studies and applications to biomedical and genomic data. The overall message is that high-dimensional modeling should not be viewed simply as a search for the smallest predictive model. Effective analysis requires careful consideration of correlation, weak signals, selection uncertainty, prediction, and post-selection estimation. I will conclude by discussing open methodological questions and potential directions for integrating machine-learning screening, regularization, shrinkage, and interpretable statistical inference in modern high-dimensional data analysis.

Tisdag 12 maj 2026, 15.00-17.00, Stanislas Muhinyuza, Linn茅universitetet

Title: The Risk Aversion Coefficient in the Tangency Portfolio: Statistical Insights from Normal and Skew-Normal Models

Sammanfattning: The paper investigates the distributional properties of the sample estimator of the risk aversion coefficient in the tangency portfolio under two asset return models. The first model assumes that returns are independent and follow a multivariate normal distribution. The second model utilizes a matrix-variate closed skew-normal distribution to account for potential asymmetry and fat tails in the data. For both models, we derive the stochastic representation, as well as the mean, variance, and high-dimensional asymptotic distribution of the sample estimator. In addition, under the normality assumption, we obtain explicit expressions for the density and characteristic functions. The high-dimensional framework considers scenarios in which both the number of assets $k_n=k(n)$ and the sample size $n$ tend to infinity, with their ratio $c_n=k_n/n \to c \in (0,1)$. A simulation study confirms that the proposed asymptotic distributions closely approximate the exact distributions even in finite samples, under both models.

Tisdag 14 april, 15.15-16.00, Joni Virta, University of Turku

Titel: Some perspectives on separable covariance matrices

Sammanfattning: Separable (Kronecker) covariance structures are a widely used model for data with multiple modalities, e.g., samples of images or observations indexed by both temporal and measurement dimensions. In this talk, we give an overview of the separable covariance framework, covering its motivation, properties, and standard approaches to its estimation. We then discuss the problem of testing the separability assumption, including a recent extension to elliptical matrix-variate data. Finally, we explore Kronecker-core decompositions as a diagnostic tool for understanding deviations from separability. The talk assumes no prior familiarity with the topic.

Tisdag 25 november, 15.15-17.00, Jean de Dieu Niyigena, University of Rwanda

Titel: Misclassification probability approximation for a quadratic classifier with repeated measurements

Sammanfattning: In classification, any decision rule involves a risk of misclassification. We study this problem for two populations with unequal covariance matrices and repeated measurements. A quadratic classification rule is derived for the growth curve model, and the unknown parameters are estimated. Using these estimators, we compute the moments of the quadratic classifier and employ an Edgeworth-type expansion to approximate the misclassification probabilities. Numerical simulations compare the probabilities obtained using true and estimated mean parameters, as well as those computed via Monte Carlo simulations. The results show that misclassification decreases as the separation between the two groups grows, demonstrating improved classification accuracy for well-separated populations.

Tisdag 10 juni, 15.15-17.00, Nestor Parolya, Delft University of Technology

Titel: Resurrecting pseudo-inverses: Asymptotic properties of large dimensional Moore-Penrose and Ridge-type inverses with applications

Sammanfattning: In this talk, we discuss high-dimensional asymptotic properties of the Moore-Penrose inverse and, as a byproduct, of various ridge-type inverses of the sample covariance matrix. In particular, the analytical expressions of the asymptotic behavior of the weighted sample trace moments of generalized inverse matrices are deduced in terms of the partial exponential Bell polynomials which can be easily computed in practice. The asymptotic results are obtained without assumption of normality and in the high-dimensional asymptotic regime. Our findings provide universal methodology for construction of fully data-driven improved shrinkage estimators of the precision matrix, optimal portfolio weights and beyond. It is found that the Moore-Penrose inverse acts asymptotically as a certain regularizer of the true covariance matrix and it seems that its proper transformation (shrinkage) performs similarly to or even outperforms the existing benchmarks in many applications, while keeping the computational time as minimal as possible.

Tisdag 8 april, 15.15, Joni Virta, University of Turku (Finland)

Titel: Unsupervised linear discrimination using skewness

Sammanfattning: It is known that, in Gaussian two-group separation, the optimally discriminating projection direction can be estimated without any knowledge on the group labels. In this presentation, we (a) motivate this estimation problem, and (b) gather several unsupervised estimators based on skewness and derive their limiting distributions. As one of our main results, we show that all affine equivariant estimators of the optimal direction have proportional asymptotic covariance matrices, making their comparison straightforward. We use simulations to verify our results and to inspect the finite-sample behaviors of the estimators.

Onsdag 11 september 2024, Shuangzhe Liu, University of Canberra, Australia

Titel: On heavy-tailed matrix variate regression models and statistical diagnostics

Sammanfattning: Matrix variate distributions and matrix regression models are powerful tools for analysing multivariate data with inherent matrix structure. These methods extend traditional univariate and multivariate techniques to handle more complex data structures, such as those found in genomics, neuroscience, and image analysis. In this talk, we introduce a framework for regression models under heavy-tailed matrix variate distributions. We begin by discussing several matrix variate distributions and then explore the general linear model under the matrix variate normal distribution, along with its relevant variations based on heavy-tailed distributions. Additionally, we cover important sensitivity analysis and statistical diagnostics for these models, highlighting potential future research problems and applications. Our goal is to provide insights into the theoretical and practical aspects of heavy- tailed matrix variate regression models, paving the way for further advancements in this area.

Tisdag 2 april 2024, Magnus Herberthson, Matematiska institutionen, Linköpings universitet

Titel: The central limit theorem for random walks on bounded domains

Sammanfattning: The standard central limit theorem typically assumes independent identically distributed (i.i.d.) random variabels X_i (with E[X_i]=0 and finite variance V[X_i]). A scaled average of N terms will then converge to a normal distribution as N -> oo, and the variance of this normal distribution is directly related to V[X_i].
We consider a random walk in a bounded domain Omega (for simplicity in the in the plane) which will imply that the random walk variables X_i are not any longer
independent. A central limit theorem still ensures a limiting distribution for the rescaled averages as the number of terms increases, but now the covariance matrix of the limiting distribution is not so obvious. We will discuss how this covariance matrix is given by the geometry of the bounding domain Omega.

Tisdag 13 juni 2023, Nestor Parolya, Delft University of Technology

Titel: Logarithmic law of large random correlation matrices

Sammanfattning:  Consider a random vector $\mathbf{y}=\bm{\Sigma}^{1/2}\mathbf{x}$, where the $p$ elements of the vector $\mathbf{x}$ are i.i.d. real-valued random variables with zero mean and finite fourth moment, and $\bm{\Sigma}^{1/2}$ is a deterministic $p\times p$ matrix such that the eigenvalues of the population correlation matrix $\mathbf{R}$ of $\mathbf{y}$ are uniformly bounded away from zero and infinity. In this paper, we find that the log determinant of the sample correlation matrix $\hat{\mathbf{R}}$ based on a sample of size $n$ from the distribution of $\mathbf{y}$ satisfies a CLT (central limit theorem) for $p/n\to \gamma\in (0, 1]$ and $p\leq n$. Explicit formulas for the asymptotic mean and variance are provided.

In case the mean of $\mathbf{y}$ is unknown, we show that after re-centering by the empirical mean the obtained CLT holds with a shift in the asymptotic mean. This result is of independent interest in both large dimensional random matrix theory and high-dimensional statistical literature of large sample correlation matrices for non-normal data. Finally, the obtained findings are applied for testing of uncorrelatedness of $p$ random variables. Surprisingly, in the null case $\mathbf{R} =\mathbf{I}$, the test statistic becomes distribution-free and we show analytically that the obtained CLT also holds if the moments of order four do not exist at all, which conjectures a promising and robust test statistic for heavy-tailed high-dimensional data.

Tisdag 7 februari 2023, Annika Lang, Chalmers University of Technology

Titel: Simulation of random fields on Riemannian manifolds

Sammanfattning: Random fields are important building blocks in spatial models disturbed by randomness such as solutions to stochastic partial differential equations. The fast simulation of random fields is therefore crucial for efficient algorithms in uncertainty quantification. In this talk I present numerical methods for Gaussian random fields on Riemannian manifolds and discuss their convergence. Simulations illustrate the theoretical findings. This talk is based on joint work with Erik Jansson, Mihály Kovács, and Mike Pereira.
Location: Online via Zoom.

Onsdag 7 december 2022, Daniel Klein, Pavol Jozef Šafárik University, Slovakien (i samarbete med Ivan 沤e啪ula)

Titel: Multiple testing of mean values in multivariate data with BCS variance structure

Sammanfattning: A common problem in multivariate data is that the number of unknown parameters in a model can be close or even higher than sample size. This may cause problems in statistical inference. Therefore, models with special variance structure are studied by many authors, where the number of covariance parameters is reduced by some restrictions on parameter space. One of possible structure could be so called block compound symmetry (BCS) structure. In this talk we will be studying estimation and testing such a structure as well as test of mean values assuming BCS structure.

Tisdag 11 oktober 2022, Solomon W. Harrar, University of Kentucky, USA

Titel: Nonparametric Finite Mixture: Applications in Contaminated Trials

Sammanfattning: Investigating the differential effect of treatments in groups defined by patient characteristics is of paramount importance in personalized medicine. Group membership is typically determined by diagnostic devices or biomarkers, but such tools are not perfectly accurate. The impact of diagnostic misclassification or contamination in statistical inference has received only little attention in the literature. This work addresses the problem in a fully nonparametric setting. Nonparametric finite mixture is proposed for estimating and testing of meaningful yet nonparametric treatment effects. Consistent estimators and asymptotic distributions are provided for the misclassification error rates as well as treatment effects. Numerical examples show significant advantages of the proposed method in terms of bias reduction, coverage probability and power. The application of the proposed method is illustrated with data from asthma and sleep deprivation studies.

Tisdag 4 februari 2020, Raazesh Sainudiin, Uppsala universitet

Titel: Minimum distance histograms with universal performance guarantees

Sammanfattning: We present a data-adaptive multivariate histogram estimator of an unknown density f based on n independent samples from it. Such histograms are based on binary trees called regular pavings (RPs). RPs represent a computationally convenient class of simple functions that remain closed under addition and scalar multiplication. Unlike other density estimation methods, including various regularization and Bayesian methods based on the likelihood, the minimum distance estimate (MDE) is guaranteed to be within an L1distance bound from f for a given n, no matter what the underlying f happens to be, and is thus said to have universal performance guarantees (Devroye and Lugosi, Combinatorial methods in density estimation. Springer, New York, 2001). Using a form of tree matrix arithmetic with RPs, we obtain the first generic constructions of an MDE, prove that it has universal performance guarantees and demonstrate its performance with simulated and real-world data. Our main contribution is a constructive implementation of an MDE histogram that can handle large multivariate data bursts using a tree-based partition that is computationally conducive to subsequent statistical operations.

Tisdag 15 oktober 2019, Kristoffer Lindensjö, Uppsala universitet

Titel: Moment constrained optimal dividends: precommitment & consistent planning

Sammanfattning: A moment constraint that limits the number of dividends in the optimal dividend problem is suggested. This leads to a new type of time-inconsistent stochastic impulse control problem. First, the optimal solution in the precommitment sense is derived. Second, the problem is formulated as an intrapersonal sequential dynamic game in line with Strotz' consistent planning. In particular, the notions of pure dividend strategies and a (strong) subgame perfect Nash equilibrium are adapted. An equilibrium is derived using a smooth fit condition. The equilibrium is shown to be strong. The uncontrolled state process is a fairly general diffusion.

Tisdag 17 september 2019, Jimmy Olsson, KTH

Titel: Bayesian learning of weakly structural Markov graph laws using sequential Monte Carlo methods

Sammanfattning: We shall discuss a sequential Monte Carlo-based approach to approximation of weakly structural Markov graph laws on spaces of decomposable graphs, or, more generally, spaces of junction (clique) trees associated with such graphs. In particular, we apply a particle Gibbs version of the algorithm to Bayesian structure learning in decomposable graphical models, where the target distribution is a junction tree posterior distribution. Moreover, we use the proposed algorithm for exploring certain fundamental combinatorial properties of decomposable graphs, e.g. clique size distributions. Our approach requires the design of a family of proposal kernels, so-called junction tree expanders, which expand junction trees by connecting randomly new nodes to the underlying graphs. The performance of the estimators is illustrated through a collection of numerical examples demonstrating the feasibility of the suggested approach in high-dimensional domains.

Tisdag 7 maj 2019, Chun-Biu Li, Stockholms universitet

Titel: Statistical Learning as a Compression Problem from the Information Theory Perspective

Sammanfattning: Although it was introduced in the context of communication theory, modern information theory provides us with a nonparametric probabilistic framework for statistical learning free from a priori assumption on the underlying statistical model. In this talk, I will discuss some of the information theory based methods for unsupervised and supervised learning. In particular, the soft (fuzzy) clustering problem in unsupervised learning can be viewed as a tradeoff between data compression and minimizing the distortion of the data. Similarly, modeling in supervised learning can be treated as a tradeoff between compression of the predictor variables and retaining the relevant information about the response variable. To illustrate the usage of these methods, some applications in biophysical problems and time series analysis will be addressed in the talk.

Tisdag 5 mars 2019, Peter Olofsson, Högskolan i Jönköping

Titel: Muller's Ratchet in Populations Doomed to Extinction

Sammanfattning: Muller's ratchet is the process by which asexual populations accumulate deleterious mutations in an irreversible manner. Most mathematical models have been of the Wright-Fisher type with fixed population size and relative fitness. In contrast, we use a branching process model with absolute fitness, leading to unavoidable extinction. Individuals are divided into classes depending on how many mutations they have accumulated, and we give results for the rate of the ratchet and the size of the fittest class.