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We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…
While nowadays most gradient-based optimization methods focus on exploring the high-dimensional geometric features, the random error accumulated in a stochastic version of any algorithm implementation has not been stressed yet. In this…
In the context of state-space models, skeleton-based smoothing algorithms rely on a backward sampling step which by default has a $\mathcal O(N^2)$ complexity (where $N$ is the number of particles). Existing improvements in the literature…
In this paper, we establish an initial theory regarding the Second Order Asymptotical Regularization (SOAR) method for the stable approximate solution of ill-posed linear operator equations in Hilbert spaces, which are models for linear…
In [8] (Nakagawa, et.al., IEEE Trans. IT, 2021), we investigated the convergence speed of the Arimoto-Blahut algorithm. In [8], the convergence of the order $O(1/N)$ was analyzed by focusing on the second-order nonlinear recurrence formula…
We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…
We present Zeroth-order Riemannian Averaging Stochastic Approximation (\texttt{Zo-RASA}) algorithms for stochastic optimization on Riemannian manifolds. We show that \texttt{Zo-RASA} achieves optimal sample complexities for generating…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any…
We introduce a computationally efficient and accurate reduced order modelling approach for the optimization of spatiotemporally chaotic systems. The proposed method combines quantized local reduced order modelling with adjoint-based…
Sequential Monte Carlo (SMC) methods are a class of techniques to sample approximately from any sequence of probability distributions using a combination of importance sampling and resampling steps. This paper is concerned with the…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
Variance-reduced stochastic gradient methods have gained popularity in recent times. Several variants exist with different strategies for the storing and sampling of gradients and this work concerns the interactions between these two…
This paper develops a unified framework, based on iterated random operator theory, to analyze the convergence of constant stepsize recursive stochastic algorithms (RSAs). RSAs use randomization to efficiently compute expectations, and so…
Subsampling is an effective approach to alleviate the computational burden associated with large-scale datasets. Nevertheless, existing subsampling estimators incur a substantial loss in estimation efficiency compared to estimators based on…
Class imbalance problem is commonly faced while developing machine learning models for real-life issues. Due to this problem, the fitted model tends to be biased towards the majority class data, which leads to lower precision, recall, AUC,…
Assessing consistency in Pairwise Comparison Matrices (PCMs) within the Analytical Hierarchy Process (AHP) poses significant challenges when using the traditional Consistency Ratio (CR) method. This study introduces a novel alternative that…
The challenge of Out-of-Distribution (OOD) generalization poses a foundational concern for the application of machine learning algorithms to risk-sensitive areas. Inspired by traditional importance weighting and propensity weighting…
In Monte-Carlo methods the Markov processes used to sample a given target distribution usually satisfy detailed balance, i.e. they are time-reversible. However, relatively recent results have demonstrated that appropriate reversible and…