Related papers: Mean-preserving rounding integer-valued ARMA model…
The promise of machine learning has been explored in a variety of scientific disciplines in the last few years, however, its application on first-principles based computationally expensive tools is still in nascent stage. Even with the…
In this paper, we first propose a new extended mixture model of residual lifetime distributions. We show that this model is suitable in modeling residual lifetime in some practical situations. Several closure properties of some well-known…
In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As computers and…
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…
Contemporary time series analysis has seen more and more tensor type data, from many fields. For example, stocks can be grouped according to Size, Book-to-Market ratio, and Operating Profitability, leading to a 3-way tensor observation at…
We introduce a new class of automated market maker (AMM), the \emph{partially active automated market maker} (PA-AMM). PA-AMM divides its reserves into two parts, the active and the passive parts, and uses only the active part for trading.…
In object segmentation by active contours, the initial contour is often required. Conventionally, the initial contour is provided by the user. This paper extends the conventional active contour model by incorporating feature matching in the…
An approach to the modelling of volatile time series using a class of uniformity-preserving transforms for uniform random variables is proposed. V-transforms describe the relationship between quantiles of the stationary distribution of the…
Probability density models based on deep networks have achieved remarkable success in modeling complex high-dimensional datasets. However, unlike kernel density estimators, modern neural models do not yield marginals or conditionals in…
Shrinkage estimators of covariance are an important tool in modern applied and theoretical statistics. They play a key role in regularized estimation problems, such as ridge regression (aka Tykhonov regularization), regularized discriminant…
As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…
We mechanize the fundamental properties of a rounding error model for floating-point arithmetic based on relative precision, a measure of error proposed as a substitute for relative error in rounding error analysis. A key property of…
Several cellular automata (CA) models have been developed to simulate self-organization of multiple levels of structures. However, they do not obey microscopic reversibility and conservation laws. In this paper, we describe the construction…
Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial,…
We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of multivariate ARMA equations with independent and identically distributed noise. For general ARMA$(p,q)$ equations these conditions are…
Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for…
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…
We study the characteristic function and moments of the integer-valued random variable $\lfloor X+\alpha\rfloor$, where $X$ is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded…
Order-Agnostic autoregressive models have demonstrated strong performance in deep generative modeling, yet their use in settings with incomplete data remains largely unexplored. In this work, we reinterpret them through the lens of missing…
In this paper, we give a AR$(1)$ type of characterization covering all multivariate strictly stationary processes indexed by the set of integers. Consequently, we derive continuous time algebraic Riccati equations for the parameter matrix…