Related papers: Probability models characterized by generalized re…

This paper considers generalizations of the functional equations that characterize the lack-of-memory properties at univariate and bivariate levels. Specifically, we extend the univariate functional equation introduced by Kaminsky (1983)…

Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…

Prime number multiplet classifications and patterns are extended to negative integers. The extension from prime numbers to single prime powers is also studied. Prime number septets at equal distance are given. It is also shown that each…

We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and…

We identify a phenomenon, which we refer to as multi-model forgetting, that occurs when sequentially training multiple deep networks with partially-shared parameters; the performance of previously-trained models degrades as one optimizes a…

Suppose a string $X_1^n=(X_1,X_2,...,X_n)$ generated by a memoryless source $(X_n)_{n\geq 1}$ with distribution $P$ is to be compressed with distortion no greater than $D\geq 0$, using a memoryless random codebook with distribution $Q$. The…

We will see that key concepts of number theory can be defined for arbitrary operations. We give a generalized distributivity for hyperoperations (usual arithmetic operations and operations going beyond exponentiation) and a generalization…

To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…

As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…

We consider an action of a compact group whose dual is archimedean linearly ordered or a direct product (or sum) of such groups on a von Neumann algebra, M. We define the generalized Hardy subspace of the Hilbert space of a standard…

Paraphrase Identification is a fundamental task in Natural Language Processing. While much progress has been made in the field, the performance of many state-of-the-art models often suffer from distribution shift during inference time. We…

We consider a generalisation of the classical Lehmer problem about the parity distribution of an integer and its modular inverse. We use some known estimates of exponential sums to study a more general question of simultaneous distribution…

We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the…

In the partially-observed outcome setting, a recent set of proposals known as "prediction-powered inference" (PPI) involve (i) applying a pre-trained machine learning model to predict the response, and then (ii) using these predictions to…

Data uncertainty in practical person reID is ubiquitous, hence it requires not only learning the discriminative features, but also modeling the uncertainty based on the input. This paper proposes to learn the sample posterior and the class…

Generalized linear models are often assumed to fit propensity scores, which are used to compute inverse probability weighted (IPW) estimators. In order to derive the asymptotic properties of IPW estimators, the propensity score is supposed…

A lossy compression algorithm for binary redundant memoryless sources is presented. The proposed scheme is based on sparse graph codes. By introducing a nonlinear function, redundant memoryless sequences can be compressed. We propose a…

We consider the notions of the replicators, including the duplicator and triplicator, of a binary operad. As in the closely related notions of di-Var-algebra and tri-Var-algebra in [14], they provide a general operadic definition for the…

A real \alpha is called recursively enumerable ("r.e." for short) if there exists a computable, increasing sequence of rationals which converges to \alpha. It is known that the randomness of an r.e. real \alpha can be characterized in…

The Sparse Distributed Memory proposed by Pentii Kanerva (SDM in short) was thought to be a model of human long term memory. The architecture of the SDM permits to store binary patterns and to retrieve them using partially matching…