Related papers: On VC-density over indiscernible sequences
Every adapted absolutely continuous process has a predictable density. The set of adapted absolutely continuous processes equals the set of time integrals of progressive or predictable pathwise locally integrable processes.
Let $k$ be an integer which is the difference between prime numbers infinitely often. It is known that there are infinitely many such $k$ and, in this paper, we give a new unconditional proof that these $k$ have positive density and improve…
Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…
We investigate the conditions under which unconditional dense coding can be achieved using continuous variable entanglement. We consider the effect of entanglement impurity and detector efficiency and discuss experimental verification. We…
In computer science, combinatorics, and model theory, the VC dimension is a central notion underlying far-reaching topics such as error rate for decision rules, combinatorial measurements of classes of finite structures, and neo-stability…
Video Individual Counting (VIC) has received increasing attention for its importance in intelligent video surveillance. Existing works are limited in two aspects, i.e., dataset and method. Previous datasets are captured with fixed or rarely…
Estimated density is often interpreted as indicating how typical a sample is under a model. Yet deep models trained on one dataset can assign higher density to simpler out-of-distribution (OOD) data than to in-distribution test data. We…
We consider the distribution of a graph invariant of central similarity proximity catch digraphs (PCDs) based on one dimensional data. The central similarity PCDs are also a special type of parameterized random digraph family defined with…
Given a prime number $p$, the study of divisibility properties of a sequence $c(n)$ has two contending approaches: $p$-adic valuations and superconcongruences. The former searches for the highest power of $p$ dividing $c(n)$, for each $n$;…
I consider two problems in machine learning and statistics: the problem of estimating the joint probability density of a collection of random variables, known as density estimation, and the problem of inferring model parameters when their…
For integers $k\geq 3,d\geq 2,$ we consider the abundance property of pinned $k$-point patterns occurring in $E\subseteq \mathbb R^d$ with positive upper density $\delta(E)$. We show that for any fixed $k$-point pattern $V$, there is a set…
We introduce the notion of density of a rational language with respect to a sequence of probability measures. We prove that if $(\mu_n)$ is a sequence of Bernoulli measures converging to a positive Bernoulli measure $\overline{\mu}$, the…
Given a prime number $p$, the study of divisibility properties of a sequence $c(n)$ has two contending approaches: $p$-adic valuations and superconcongruences. The former searches for the highest power of $p$ dividing $c(n)$, for each $n$;…
We show that a persistence module (for a totally ordered indexing set) consisting of finite-dimensional vector spaces is a direct sum of interval modules. The result extends to persistence modules with the descending chain condition on…
Assessing the predictive uncertainty of deep neural networks is crucial for safety-related applications of deep learning. Although Bayesian deep learning offers a principled framework for estimating model uncertainty, the common approaches…
Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical…
If $T$ has dependent dividing, then the burden agrees with the dp-rank witnessed by NIP formulas. We use this observation to prove that if $T$ has dependent dividing, then the burden is sub-additive. We also state a connection between the…
We generally study the density of eigenvalues in unitary ensembles of random matrices from the recurrence coefficients with regularly varying conditions for the orthogonal polynomials. First we calculate directly the moments of the density.…
A recurrence equation is a discrete integrable equation whose solutions are all periodic and the period is fixed. We show that infinitely many recurrence equations can be derived from the information about invariant varieties of periodic…
Applications of Implicit Neural Representations (INRs) have emerged as a promising deep learning approach for compactly representing large volumetric datasets. These models can act as surrogates for volume data, enabling efficient storage…