arXiv research

We study fundamental groups of toroidal compactifications of non compact ball quotients and show that the Shafarevich conjecture on holomorphic convexity for these complex projective manifolds is satisfied in dimension 2 provided the corresponding lattice is arithmetic and small enough. The method is to show that the A…

Bayesian methods often misinterpret data and asymptotic concepts.

Anabelian geometry reformulated using Hodge theory for hyperbolic curves.

Tangle machines are a topologically inspired diagrammatic formalism to describe information flow in networks. This paper begins with an expository account of tangle machines motivated by the problem of describing `covariance intersection' fusion of Gaussian estimators in networks. It then gives two examples in which ta…

An orbifold is a Morita equivalence class of a proper {\' e}tale Lie groupoid. A unitary equivalence class of spectral triples over the algebra of smooth invariant functions are associated with any compact spin orbifold. In the case of an effective spin orbifold we construct a collection of spectral triples over the sm…

Modern classification problems frequently present mild to severe label imbalance as well as specific requirements on classification characteristics, and require optimizing performance measures that are non-decomposable over the dataset, such as F-measure. Such measures have spurred much interest and pose specific chall…

We consider the partial observability model for multi-armed bandits, introduced by Mannor and Shamir. Our main result is a characterization of regret in the directed observability model in terms of the dominating and independence numbers of the observability graph. We also show that in the undirected case, the learner …

This paper investigates arbitrage chains involving four currencies and four foreign exchange trader-arbitrageurs. In contrast with the three-currency case, we find that arbitrage operations when four currencies are present may appear periodic in nature, and not involve smooth convergence to a "balanced" ensemble of exc…

Feature selection from wide datasets leads to misleading results.

Survey of methods for computing volumes of moduli spaces.

Develops methods for dynamic pricing in incomplete data settings.

The paper explores tail diversification in financial markets using entropy and mutual information.

Confounding variables are a well known source of nuisance in biomedical studies. They present an even greater challenge when we combine them with black-box machine learning techniques that operate on raw data. This work presents two case studies. In one, we discovered biases arising from systematic errors in the data g…

Geographic diversification is fundamental to risk mitigation among investors and insurers of housing, mortgages, and mortgage-related derivatives. To characterize diversification potential, we provide estimates of integration, spatial correlation, and contagion among US metropolitan housing markets. Results reveal a hi…

The pattern theory of Grenander is a mathematical framework where patterns are represented by probability models on random variables of algebraic structures. In this paper, we review three families of probability models, namely, the discriminative models, the descriptive models, and the generative models. A discriminat…

Framework combines adversarial training and provable robustness for neural networks.

Lecture notes on linear neural networks for deep learning optimization and generalization.

HIVE-COTE v1.0 improves time series classification with enhanced usability.

In healthcare, patient risk stratification models are often learned using time-series data extracted from electronic health records. When extracting data for a clinical prediction task, several formulations exist, depending on how one chooses the time of prediction and the prediction horizon. In this paper, we show how…

Integration of the form $\int_a^\infty {f(x)w(x)dx}$, where $w(x)$ is either $\sin (ω{\kern 1pt} x)$ or $\cos (ω{\kern 1pt} x)$, is widely encountered in many engineering and scientific applications, such as those involving Fourier or Laplace transforms. Often such integrals are approximated by a numerical integration…

In Euclidean geometry, all metric notions (arc length for curves, the first fundamental form for surfaces, etc.) are derived from the Euclidean inner product on tangent vectors, and this inner product is preserved by the full symmetry group of Euclidean space (translations, rotations, and reflections). In equiaffine ge…

For any Lie groupoid we construct an analytic index morphism taking values in a modified $K-theory$ group which involves the convolution algebra of compactly supported smooth functions over the groupoid. The construction is performed by using the deformation algebra of smooth functions over the tangent groupoid constru…

The use of synthetic data generated by Generative Adversarial Networks (GANs) has become quite a popular method to do data augmentation for many applications. While practitioners celebrate this as an economical way to get more synthetic data that can be used to train downstream classifiers, it is not clear that they re…

Paper warns of metric deformation in manifold learning, leading to incorrect answers.

sktime is an open source, Python based, sklearn compatible toolkit for time series analysis developed by researchers at the University of East Anglia (UEA), University College London and the Alan Turing Institute. A key initial goal for sktime was to provide time series classification functionality equivalent to that a…

This paper investigates how two important sources of risk -- market tail risk and extreme market volatility risk -- are priced into the cross-section of asset returns across various investment horizons. To identify such risks, we propose a quantile spectral beta representation of risk based on the decomposition of cova…

Holomorphic functions from knot complements link to quantum modular forms.

Model compares altruism and individualism in wealth dynamics.

Time series classification (TSC) is the problem of learning labels from time dependent data. One class of algorithms is derived from a bag of words approach. A window is run along a series, the subseries is shortened and discretised to form a word, then features are formed from the histogram of frequency of occurrence …

GANs can bias synthetic data, affecting minority and female faces.

Analyzes the Hessian of ReLU networks, proving skewed eigenvalue distribution.

Dynamic pricing improves DeFi lending efficiency by reducing regret to logarithmic levels.

Two types of differentials are shown equivalent for compactifying moduli spaces.

We propose a novel approach to sentiment data filtering for a portfolio of assets. In our framework, a dynamic factor model drives the evolution of the observed sentiment and allows to identify two distinct components: a long-term component, modeled as a random walk, and a short-term component driven by a stationary VA…

Researchers expand on best subset selection theory, identifying key complexities.

Study covers of surfaces, showing types and properties.

A {\em solvable} cover of a graph is a regular cover whose covering transformation group is solvable. In this paper, we show that a solvable cover of a graph can be decomposed into layers of abelian covers, and also, a lift of a given automorphism of the base graph of a solvable cover can be decomposed into layers of l…

AugBagg improves random forest accuracy with added noise variables.

After showing that a covering space of surface bundles over $S^1$ factors as a `covering of fibers' followed by a `power covering', we prove that, for torus bundles, power coverings do not lower Heegaard genus, and that fiber coverings lower the genus only in special cases.

This work develops a unified framework for RLHF with general $f$-divergence regularization.

In "Rips complexes and covers in the uniform category" \cite{Rips} the authors define, following James \cite{J}, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform covering maps and generalized uniform covering maps are given…

A foliation of a manifold M is called R-covered if its lift to the universal cover of M has space of leaves R. We show that there are many graph manifolds which admit taut foliations, but which do not admit any R-covered foliations. On the other hand, we show that these manifolds all have finite covers admitting R-cove…

The paper studies which branched covers can be lifted to braided embeddings.

We discuss construction of coverings of the unit ball of a finite dimensional Banach space. The well known technique of comparing volumes gives upper and lower bounds on covering numbers. This technique does not provide a construction of good coverings. Here we apply incoherent dictionaries for construction of good cov…

The paper tackles learning from imperfect human feedback, especially in dueling bandit problems.

State-of-the-art results on image recognition tasks are achieved using over-parameterized learning algorithms that (nearly) perfectly fit the training set and are known to fit well even random labels. This tendency to memorize the labels of the training data is not explained by existing theoretical analyses. Memorizati…

The paper details folding of branched covers of the 3-sphere over knots.

We introduce a framework for coverings of noncommutative spaces. Moreover, we study noncommutative coverings of irrational quantum tori and characterize all such coverings that are connected in a reasonable sense.