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Many mathematical modelling tasks (such as in Economics and Finance) are informed by data that is "found" rather than being the result of carefully designed experiments. This often results in data series that are short, noisy,…
This study addresses a fundamental, yet overlooked, gap between standard theory and empirical modelling practices in the OLS regression model $\boldsymbol{y}=\boldsymbol{X\beta}+\boldsymbol{u}$ with collinearity. In fact, while an estimated…
Statistical learning methods typically assume that the training and test data originate from the same distribution, enabling effective risk minimization. However, real-world applications frequently involve distributional shifts, leading to…
New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…
Dynamic inference problems in autoregressive (AR/ARMA/ARIMA), exponential smoothing, and navigation are often formulated and solved using state-space models (SSM), which allow a range of statistical distributions to inform innovations and…
In biomedical studies, it is often desirable to characterize the interactive mode of multiple disease outcomes beyond their marginal risk. Ising model is one of the most popular choices serving for this purpose. Nevertheless, learning…
Interval censored data commonly arise in medical studies when the event time of interest is only known to lie within an interval. In the presence of a cure subgroup, conventional mixture cure models typically assume a logistic model for the…
Sure Independence Screening is a fast procedure for variable selection in ultra-high dimensional regression analysis. Unfortunately, its performance greatly deteriorates with increasing dependence among the predictors. To solve this issue,…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
The classical functional linear regression model (FLM) and its extensions, which are based on the assumption that all individuals are mutually independent, have been well studied and are used by many researchers. This independence…
Symmetric Positive Definite (SPD) matrices have received wide attention in machine learning due to their intrinsic capacity to encode underlying structural correlation in data. Many successful Riemannian metrics have been proposed to…
We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
Extremile regression, as a least squares analog of quantile regression, is potentially useful tool for modeling and understanding the extreme tails of a distribution. However, existing extremile regression methods, as nonparametric…
We propose the -- to the best of our knowledge -- first fully functional implementation of the ``Separation by a Convex Body'' (SCB) approach first outlined in Grzybowski et al. [1] for classification, separating two data sets using an…
Reliability of SLAM systems is considered one of the critical requirements in modern autonomous systems. This directed the efforts to developing many state-of-the-art systems, creating challenging datasets, and introducing rigorous metrics…
Causal discovery from observational and interventional data is challenging due to limited data and non-identifiability: factors that introduce uncertainty in estimating the underlying structural causal model (SCM). Selecting experiments…
For the past two decades, single-index model, a special case of projection pursuit regression, has proven to be an efficient way of coping with the high dimensional problem in nonparametric regression. In this paper, based on weakly…
Linear regression with normally distributed errors - including particular cases such as ANOVA, Student's t-test or location-scale inference - is a widely used statistical procedure. In this case the ordinary least squares estimator…
We derive bounds on the sample complexity of empirical risk minimization (ERM) in the context of minimizing non-convex risks that admit the strict saddle property. Recent progress in non-convex optimization has yielded efficient algorithms…