Related papers: KL-randomness and effective dimension under strong…

The Kullback-Leibler (KL) divergence is a fundamental equation of information theory that quantifies the proximity of two probability distributions. Although difficult to understand by examining the equation, an intuition and understanding…

We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…

We consider model-based reinforcement learning in finite Markov De- cision Processes (MDPs), focussing on so-called optimistic strategies. In MDPs, optimism can be implemented by carrying out extended value it- erations under a constraint…

Dimension reduction is a technique used to transform data from a high-dimensional space into a lower-dimensional space, aiming to retain as much of the original information as possible. This approach is crucial in many disciplines like…

This paper studies the multivariate approximation of functions in weighted Korobov spaces using multiple rank-1 lattice rules. It has been shown by K\"{a}mmerer and Volkmer (2019) that algorithms based on multiple rank-1 lattices achieve…

In this paper, we present a conjecture on the degree of unipotent characters in the cohomology of particular Deligne-Lusztig varieties for groups of Lie type, and derive consequences of it. These degrees are a necessary piece of data in the…

Score-matching generative models have proven successful at sampling from complex high-dimensional data distributions. In many applications, this distribution is believed to concentrate on a much lower $d$-dimensional manifold embedded into…

The Kullback-Leibler (KL) divergence is frequently used in data science. For discrete distributions on large state spaces, approximations of probability vectors may result in a few small negative entries, rendering the KL divergence…

We explicitly describe the Lie algebras $M_L$ of ladder matrices in $M_n$ associate with dominant upper triangular ladders $L$, and completely characterize the derivations of these $M_L$ over a field $F$ with $char(F) \neq 2$. We also…

We study the maximum likelihood (ML) degree of linear concentration models in algebraic statistics. We relate it to an intersection problem on the variety of complete quadrics. This allows us to provide an explicit, basic, albeit of high…

By analysing the structure of the associated graded ring with respect to certain filtrations, we deduce a number of good properties of iterated local skew power series rings over appropriate base rings. In particular, we calculate the Krull…

Bennett's notion of depth is usually considered to describe the usefulness and internal organization of the information encoded into an object such as an infinite binary sequence. We consider a natural way to relativize the notion of depth…

Adapting a result of Bazhenov, Kalimullin, and Yamaleev, we show that if a Turing degree $\textbf{d}$ is the degree of categoricity of a computable structure $\mathcal{M}$ and is not the strong degree of categoricity of any computable…

We give a simple proof of Lee's result from [Adv. Math. 179 (2005) 554-586; arXiv:math.GT/0210213], that the dimension of the Lee variant of the Khovanov homology of a c-component link is 2^c, regardless of the number of crossings. Our…

Universal hypothesis testing refers to the problem of deciding whether samples come from a nominal distribution or an unknown distribution that is different from the nominal distribution. Hoeffding's test, whose test statistic is equivalent…

It is shown that the Ramadanov conjecture implies the Cheng conjecture. In particular it follows that the Cheng conjecture holds in dimension two.

The lower transcendence degree, introduced by J. J Zhang, is an important non-commutative invariant in ring theory and non-commutative geometry strongly connected to the classical Gelfand-Kirillov transcendence degree. For LD-stable…

We prove a new theorem of Tverberg type which confirms the conjecture of Blagojevic, Frick, and Ziegler about the existence of "balanced Tverberg partitions" (Conjecture 6.6 in, Tverberg plus constraints, Bull. London Math. Soc., 46 (2014)…

A Martin-L\"of test $\mathcal U$ is universal if it captures all non-Martin-L\"of random sequences, and it is optimal if for every ML-test $\mathcal V$ there is a $c \in \omega$ such that $\forall n(\mathcal{V}_{n+c} \subseteq…

This paper concerns the problem of classifying finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the one hand, we present an effective method to classify all $(n+1)$-dimensional real solvable…