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Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used to estimate gradients of expectations throughout machine learning and reinforcement learning; however, they are usually explained as simple mathematical tricks,…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
We consider the problem of mixed linear regression (MLR), where each observed sample belongs to one of $K$ unknown linear models. In practical applications, the proportions of the $K$ components are often imbalanced. Unfortunately, most MLR…
This paper provides a simple method to estimate both univariate and multivariate MA processes. Similar to Durbin's method, it rests on the recursive relation between the parameters of the MA process and those of its AR representation. This…
In this work we introduce the class of beta autoregressive fractionally integrated moving average models for continuous random variables taking values in the continuous unit interval $(0,1)$. The proposed model accommodates a set of…
A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed…
Efficient estimation methods for simultaneous autoregressive (SAR) models with missing data in the response variable have been well-explored in the literature. A common practice is to introduce measurement error into SAR models to separate…
We consider nonparametric estimation for functional autoregressive processes with Markov switching. First, we study the case where complete data is available; i.e. when we observe the Markov switching regime. Then we estimate the regression…
Online (also called "recursive" or "adaptive") estimation of fixed model parameters in hidden Markov models is a topic of much interest in times series modelling. In this work, we propose an online parameter estimation algorithm that…
Motivated by single-particle cryo-electron microscopy, multi-reference alignment (MRA) models the task of recovering an unknown signal from multiple noisy observations corrupted by random rotations. The standard approach,…
Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…
A Maximum Likelihood recursive state estimator is derived for non-linear and non-Gaussian state-space models. The estimator combines a particle filter to generate the conditional density and the Expectation Maximization algorithm to compute…
Restricted maximum likelihood (REML) estimation is a widely accepted and frequently used method for fitting linear mixed models, with its principal advantage being that it produces less biased estimates of the variance components. However,…
The multi-reference alignment (MRA) problem involves reconstructing a signal from multiple noisy observations, each transformed by a random group element. In this paper, we focus on the group \(\mathrm{SO}(2)\) of in-plane rotations and…
We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We…
Process Reward Models (PRMs) emerge as a promising approach for process supervision in mathematical reasoning of Large Language Models (LLMs), which aim to identify and mitigate intermediate errors in the reasoning processes. However, the…
Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in…
A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the…
Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…
While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…