Related papers: Weighted sieves with switching

Estimating parameters of mixture model has wide applications ranging from classification problems to estimating of complex distributions. Most of the current literature on estimating the parameters of the mixture densities are based on…

A sieve is constructed for twin primes at distance 4, which are of the form 3(2m+1)+/-2, and are characterized by their twin-4 rank 2m+1. It has no parity problem. Non-ranks are identified as all other odd numbers and counted using odd…

Gene-gene interactions play a crucial role in the manifestation of complex human diseases. Uncovering significant gene-gene interactions is a challenging task. Here, we present an innovative approach utilizing data-driven computational…

We study the weighted token swapping problem, in which we are given a graph on $n$ vertices, $n$ weighted tokens, an initial assignment of one token to each vertex, and a final assignment of one token to each vertex. The goal is to find a…

We consider the problem of closeness testing for two discrete distributions in the practically relevant setting of \emph{unequal} sized samples drawn from each of them. Specifically, given a target error parameter $\varepsilon > 0$, $m_1$…

Theorems of Khintchine, Groshev, Jarn\'ik, and Besicovitch in Diophantine approximation are fundamental results on the metric properties of $\Psi$-well approximable sets. These foundational results have since been generalised to the…

The marginal likelihood is a central tool for drawing Bayesian inference about the number of components in mixture models. It is often approximated since the exact form is unavailable. A bias in the approximation may be due to an incomplete…

We obtain asymptotic formulas for the $2k$th moments of partially smoothed divisor sums of the M\"obius function. When $2k$ is small compared with $A$, the level of smoothing, then the main contribution to the moments come from integers…

We show that there are infinitely many primes $p$ such that not only does $p + 2$ have at most two prime factors, but $p + 6$ also has a bounded number of prime divisors. This refines the well known result of Chen.

Sparseness of the regression coefficient vector is often a desirable property, since, among other benefits, sparseness improves interpretability. In practice, many true regression coefficients might be negligibly small, but non-zero, which…

Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…

We propose a simple method by which to choose sample weights for problems with highly imbalanced or skewed traits. Rather than naively discretizing regression labels to find binned weights, we take a more principled approach -- we derive…

In recent years, there has been an increasing demand on efficient algorithms for large scale change point detection problems. To this end, we propose seeded binary segmentation, an approach relying on a deterministic construction of…

In machine learning models, the estimation of errors is often complex due to distribution bias, particularly in spatial data such as those found in environmental studies. We introduce an approach based on the ideas of importance sampling to…

Importance weighting is a fundamental procedure in statistics and machine learning that weights the objective function or probability distribution based on the importance of the instance in some sense. The simplicity and usefulness of the…

We introduce a modification of the linear sieve whose weights satisfy strong factorization properties, and consequently equidistribute primes up to size $x$ in arithmetic progressions to moduli up to $x^{10/17}$. This surpasses the level of…

Pairwise re-ranking models predict which of two documents is more relevant to a query and then aggregate a final ranking from such preferences. This is often more effective than pointwise re-ranking models that directly predict a relevance…

Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual…

In this paper, we study the weighted difference substitutions from geometrical views. First, we give the geometric meanings of the weighted difference substitutions, and introduce the concept of convergence of the sequence of substitution…

While Bayesian methods are praised for their ability to incorporate useful prior knowledge, in practice, convenient priors that allow for computationally cheap or tractable inference are commonly used. In this paper, we investigate the…