Related papers: Strong Convergence on Weakly Logarithmic Combinato…
If $S$ is a cofinite set of positive integers, an "$S$-restricted composition of $n$" is a sequence of elements of $S$, denoted $\vec{\lambda}=(\lambda_1,\lambda_2,...)$, whose sum is $n$. For uniform random $S$-restricted compositions, the…
This paper is the second in a series of works on weak convergence of one-step schemes for solving stochastic differential equations (SDEs) with one-sided Lipschitz conditions. It is known that the super-linear coefficients may lead to a…
This work studies the average complexity of solving structured polynomial systems that are characterized by a low evaluation cost, as opposed to the dense random model previously used. Firstly, we design a continuation algorithm that…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
How do we estimate the probability of an abundant objects' formation, with minimal context or assumption about is origin? To explore this we have previously introduced the concept of pathway assembly (as pathway complexity), in a graph…
When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the…
The likelihood function represents statistical evidence in the context of data and a probability model. Considerable theory has demonstrated that evidence strength for different parameter values can be interpreted from the ratio of…
In this text we develop the formalism of products and powers of linear codes under componentwise multiplication. As an expanded version of the author's talk at AGCT-14, focus is put mostly on basic properties and descriptive statements that…
Conditional probabilities are a core concept in machine learning. For example, optimal prediction of a label $Y$ given an input $X$ corresponds to maximizing the conditional probability of $Y$ given $X$. A common approach to inference tasks…
A composite likelihood is a non-genuine likelihood function that allows to make inference on limited aspects of a model, such as marginal or conditional distributions. Composite likelihoods are not proper likelihoods and need therefore…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
The article attempts to find an algebraic formula describing the correlation coefficients between random variables and the principal components representing them. As a result of the analysis, starting from selected statistics relating to…
Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we…
This paper connects a vector-based composition model to a formal semantics, the Dependency-based Compositional Semantics (DCS). We show theoretical evidence that the vector compositions in our model conform to the logic of DCS.…
We revisit the classical concept of near-decomposability in complex systems, introduced by Herbert Simon in his foundational article The Architecture of Complexity, by developing an explicit quantitative analysis based on singular…
The converse of the Borel-Cantelli Lemma states that if $\{A_i\}_{i=1}^\infty$ is a sequence of independent events such that $\sum P(A_i)=\infty$, then almost surely infinitely many of these events will occur. Erd\H os and R\'enyi proved…
We investigate ensemble methods for prediction in an online setting. Unlike all the literature in ensembling, for the first time, we introduce a new approach using a meta learner that effectively combines the base model predictions via…
We study the behaviour of the largest components of the directed configuration model in the barely subcritical regime. We show that with high probability all strongly connected components in this regime are either cycles or isolated…