arXiv research

We prove that if an analytic subset $A$ of a linear metric space $X$ is not contained in a $σZ_ω$-subset of $X$ then for every Polish convex set $K$ with dense affine hull in $X$ the sum $A+K$ is non-meager in $X$ and the sets $A+A+K$ and $A-A+K$ have non-empty interior in the completion $\bar X$ of $X$. This implies t…

It is shown that, in the Gromov space of isometry classes of pointed proper metric spaces, the equivalence relations defined by existence of coarse quasi-isometries or being at finite Gromov-Hausdorff distance, cannot be reduced to the equivalence relation defined by any Polish action.

Milnor proved two uniqueness theorems for axiomatic (co)homology: one for pairs of compacta (1960) and another, in particular, for pairs of countable simplicial complexes (1961). We obtain their common generalization: the Eilenberg-Steenrod axioms along with Milnor's map excision axiom and a (non-obvious) common genera…

The paper deals with the program of determining the complexity of various homeomorphism relations. The homeomorphism relation on compact Polish spaces is known to be reducible to an orbit equivalence relation of a continuous Polish group action (Kechris-Solecki). It is shown that this result extends to locally compact …

New theory approximates functions between metric spaces using random probability measures.

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the…

Homotopy equivalence shown between complex and thickened versions of manifolds.

New framework for optimal transport with jumps over intermediate spaces.

Unified Kantorovich duality for multimarginal optimal transport on Polish spaces.

We introduce an universum of the Polish (=complete separable metric) space - the convex cone of distance matrices and study its geometry. It happened that the generic Polish spaces in this sense of this universum is so called Urysohn spaces defined by P.S.Urysohn in 20-th, and generic metric triple (= metric space with…

This research explores the effects of various training settings from Polish to English Statistical Machine Translation system for spoken language. Various elements of the TED parallel text corpora for the IWSLT 2013 evaluation campaign were used as the basis for training of language models, and for development, tuning …

The paper shows how to use fine shape to understand infinite-dimensional spaces.

We introduce a model of the set of all Polish (=separable complete metric) spaces: the cone $\cal R$ of distance matrices, and consider geometric and probabilistic problems connected with this object. The notion of the universal distance matrix is defined and we proved that the set of such matrices is everywhere dense …

We prove a large deviation principle for a sequence of point processes defined by Gibbs probability measures on a Polish space. This is obtained as a consequence of a more general Laplace principle for the non-normalized Gibbs measures. We consider three main applications: Conditional Gibbs measures on compact spaces, …

The article introduces a new set of Polish word embeddings, built using KGR10 corpus, which contains more than 4 billion words. These embeddings are evaluated in the problem of recognition of temporal expressions (timexes) for the Polish language. We described the process of KGR10 corpus creation and a new approach to …

Let X be a locally compact Polish space and G a non-discrete Polish ANR group. By C(X,G), we denote the topological group of all continuous maps f:X \to G endowed with the Whitney (graph) topology and by C_c(X,G) the subgroup consisting of all maps with compact support. It is known that if X is compact and non-discrete…

Feature matters for salient object detection. Existing methods mainly focus on designing a sophisticated structure to incorporate multi-level features and filter out cluttered features. We present Progressive Feature Polishing Network (PFPN), a simple yet effective framework to progressively polish the multi-level feat…

The study introduces Cayley--Abels--Rosendal graphs for Polish groups.

Graph Polish optimizes molecular structures by minimizing changes and maximizing preservation.

Study improves convergence rates for GVI under prior misspecification.

We prove that every acyclic normal one-dimensional real Ambrosio-Kirchheim current in a Polish (i.e. complete separable metric) space can be decomposed in curves, thus generalizing the analogous classical result proven by S. Smirnov in Euclidean space setting. The same assertion is true for every complete metric space …

This new research explores the effects of various training methods on a Polish to English Statistical Machine Translation system for medical texts. Various elements of the EMEA parallel text corpora from the OPUS project were used as the basis for training of phrase tables and language models and for development, tunin…

This paper shows how to construct sequential tests with power one against weakly compact sets in Polish spaces.

This research explores the effects of various training settings on a Polish to English Statistical Machine Translation system for spoken language. Various elements of the TED, Europarl, and OPUS parallel text corpora were used as the basis for training of language models, for development, tuning and testing of the tran…

The paper develops SGD for estimating operators from data.

This is an introductory text to differential geometry (written in Polish) aimed for high-school students.

Survey of recent measures of association, including a new coefficient.

Stein importance sampling is a widely applicable technique based on kernelized Stein discrepancy, which corrects the output of approximate sampling algorithms by reweighting the empirical distribution of the samples. A general analysis of this technique is conducted for the previously unconsidered setting where samples…

New algorithms reduce complexity for learning in MDPs with entropy regularization.

New cohomology functors refine classical invariants of homotopy types.

Groups of homotopy equivalences of graphs help realize compact subgroups.

Universal Language Model for Fine-tuning [arXiv:1801.06146] (ULMFiT) is one of the first NLP methods for efficient inductive transfer learning. Unsupervised pretraining results in improvements on many NLP tasks for English. In this paper, we describe a new method that uses subword tokenization to adapt ULMFiT to langua…

We show that all non-trivial continuous endomorphisms of the circle group are topologically mixing. We also show that there exists a large infinite class of continuous endomorphisms of any n-dimensional torus group which are topologically mixing. Lastly, we prove that any continuous endomorphism on an abelian polish se…

Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic programming algorithms for solving Markov decision problems. These recursive stochastic a…

Study uses deep learning for pairs trading in Polish equities, achieving profits in 2017-2019.

Log-periodic oscillations have been used to predict price trends and crashes on financial markets. So far two types of log-periodic oscillations have been associated with the real markets. The first type are oscillations which accompany a rising market and which ends in a crash. The second type oscillations, called "an…

WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the properties of metric (in particulary universal) space to the properties of distance …

We study the inter-stock correlations for the largest companies listed on Warsaw Stock Exchange and included in the WIG20 index. Our results from the correlation matrix analysis indicate that the Polish stock market can be well described by a one factor model. We also show that the stock-stock correlations tend to incr…

This paper presents a quantitative analysis of the relationship between the stock market returns and corresponding trading volumes using high- frequency data from the Polish stock market. First, for stocks that were traded for suffciently long period of time, we study the return and volume distributions and identify th…

Single tree outperforms random forest in testing accuracy.

We prove that every one-dimensional real Ambrosio-Kirchheim normal current in a Polish (i.e. complete separable metric) space can be naturally represented as an integral of simpler currents associated to Lipschitz curves. As a consequence a representation of every such current with zero boundary (i.e. a cycle) as an in…

A Polish group $G$ is called a group of quasi-invariance or a QI-group, if there exist a locally compact group $X$ and a probability measure $μ$ on $X$ such that 1) there exists a continuous monomorphism of $G$ to $X$, and 2) for each $g\in X$ either $g\in G$ and the shift $μ_g$ is equivalent to $μ$ or $g\not\in G$ and…

The statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics. Here we present a systematic study of such characteristics for the Polish stock market index WIG20 over the period 04.01.1999 - 31.10.2005 for the time lags ranging from one m…

Study on minimal torsion topological generators for mapping class groups of infinite-type surfaces.

An elementary proof shows submodular functions can be represented as measure suprema.

Non-symmetric rectangular correlation matrices occur in many problems in economics. We test the method of extracting statistically meaningful correlations between input and output variables of large dimensionality and build a toy model for artificially included correlations in large random time series.The results are t…

The paper studies convergence of kernel autocovariance operators for stationary processes.

It is proved that the isometry classes of pointed connected complete Riemannian $n$-manifolds form a Polish space, $\mathcal{M}_*^\infty(n)$, with the topology described by the $C^\infty$ convergence of manifolds. This space has a canonical partition into sets defined by varying the distinguished point into each manifo…