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Learning the joint dependence of discrete variables is a fundamental problem in machine learning, with many applications including prediction, clustering and dimensionality reduction. More recently, the framework of copula modeling has…

When modeling the distribution of a multivariate continuous random vector using the so-called \emph{copula approach}, it is not uncommon to have ties in the coordinate samples of the available data because of rounding or lack of measurement…

There are now many options for doubly robust estimation; however, there is a concerning trend in the applied literature to believe that the combination of a propensity score and an adjusted outcome model automatically results in a doubly…

We introduce innovative inference procedures for analyzing time series data. Our methodology enables density approximation and composite hypothesis testing based on Whittle's estimator, a widely applied M-estimator in the frequency domain.…

For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we…

Effective modeling of heterogeneous subpopulations presents a significant challenge due to variations in individual characteristics and behaviors. This paper proposes a novel approach to address this issue through multi-task learning (MTL)…

Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Inverse probability weighting (IPW) methods are commonly used to analyze non-ignorable missing data under the assumption of a logistic model for the missingness probability. However, solving IPW equations numerically may involve…

Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-temporal data.…

The paper concerns inference in the ill-conditioned functional response model, which is a part of functional data analysis. In this regression model, the functional response is modeled using several independent scalar variables. To verify…

Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…

This paper develops statistical methods for determining the number of components in panel data finite mixture regression models with regression errors independently distributed as normal or more flexible normal mixtures. We analyze the…

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…

We propose the Heterogeneous Thurstone Model (HTM) for aggregating ranked data, which can take the accuracy levels of different users into account. By allowing different noise distributions, the proposed HTM model maintains the generality…

We demonstrate how the uncertainty of parameter point estimates can be assessed in a maximum likelihood framework in order to prevent overfitting and erroneous detection of time-inhomogeneity. The class of models we consider are regular…

Time-varying covariates in longitudinal studies frequently evolve through reciprocal feedback, undergo role reversal, and reflect unobserved individual heterogeneity. Standard statistical frameworks often assume fixed covariate roles and…

Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system…

In linear models, omitting a covariate that is orthogonal to covariates in the model does not result in biased coefficient estimation. This in general does not hold for longitudinal data, where additional assumptions are needed to get…