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In a regular full exponential family, the maximum likelihood estimator (MLE) need not exist in the traditional sense. However, the MLE may exist in the completion of the exponential family. Existing algorithms for finding the MLE in the…
Maximum pseudo-likelihood (MPL) is a semiparametric estimation method often used to obtain the dependence parameters in copula models from data. It has been shown that despite being consistent, and in some cases efficient, MPL estimation…
Exponential moving average (EMA) has recently gained significant popularity in training modern deep learning models, especially diffusion-based generative models. However, there have been few theoretical results explaining the effectiveness…
A new family of penalty functions, adaptive to likelihood, is introduced for model selection in general regression models. It arises naturally through assuming certain types of prior distribution on the regression parameters. To study…
We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model…
In recent years several local extrema based methodologies have been proposed to investigate either the nonlinear or the nonstationary time series for scaling analysis. In the present work we study systematically the distribution of the…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…
In this paper, we introduce a new three-parameter distribution based on the combination of re-parametrization of the so-called EGNB2 and transmuted exponential distributions. This combination aims to modify the transmuted exponential…
Modern data workflows are inherently adaptive, repeatedly querying the same dataset to refine and validate sequential decisions, but such adaptivity can lead to overfitting and invalid statistical inference. Adaptive Data Analysis (ADA)…
This thesis studies high-dimensional, continuous-valued pairwise Markov Random Fields. We are particularly interested in approximating pairwise densities whose logarithm belongs to a Sobolev space. For this problem we propose the method of…
We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and…
We fit the exponent of the Pareto distribution, that is equivalent or can approximate the continuous power law distribution given a cutoff point, using linear regression (LR). We use LR on the logged variables of the empirical tail (one…
The exponential moving average (EMA) is a commonly used statistic for providing stable estimates of stochastic quantities in deep learning optimization. Recently, EMA has seen considerable use in generative models, where it is computed with…
Multivariate extreme value statistical analysis is concerned with observations on several variables which are thought to possess some degree of tail-dependence. In areas such as the modeling of financial and insurance risks, or as the…
The association between a continuous and an ordinal variable is commonly modeled through the polyserial correlation model. However, this model, which is based on a partially-latent normality assumption, may be misspecified in practice, due…
Probabilistic modelling of power systems operation and planning processes depends on data-driven methods, which require sufficiently large datasets. When historical data lacks this, it is desired to model the underlying data generation…
Robotic systems must be able to quickly and robustly make decisions when operating in uncertain and dynamic environments. While Reinforcement Learning (RL) can be used to compute optimal policies with little prior knowledge about the…
Inverse probability weighted estimators are the oldest and potentially most commonly used class of procedures for the estimation of causal effects. By adjusting for selection biases via a weighting mechanism, these procedures estimate an…
We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…
The sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M_{ij} of the stability matrix M. For globally…