arXiv research

Recent work has shown that deep generative models can assign higher likelihood to out-of-distribution data sets than to their training data (Nalisnick et al., 2019; Choi et al., 2019). We posit that this phenomenon is caused by a mismatch between the model's typical set and its areas of high probability density. In-dis…

This paper deals with both complex dynamical systems and conformal iterated function systems. We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a $d$-parameter family of such semigroups satisfies the transversality condition, then for almost every par…

New criteria for Cantor set tameness and wildness via projections.

Bayesian networks are typically faithful, with implications for causal inference.

We introduce a new algorithm, called CDER, for supervised machine learning that merges the multi-scale geometric properties of Cover Trees with the information-theoretic properties of entropy. CDER applies to a training set of labeled pointclouds embedded in a common Euclidean space. If typical pointclouds correspondin…

Distributions over rankings are used to model data in various settings such as preference analysis and political elections. The factorial size of the space of rankings, however, typically forces one to make structural assumptions, such as smoothness, sparsity, or probabilistic independence about these underlying distri…

Let g:X -> Y be a smooth (i.e. C^\infty differentiable) map between two smooth manifolds. In analogy with the case of complex polynomial functions, we say that y_0 in Y is a typical value of g if there exists an open neighbourhood U of y_0 in Y, such that the restriction g:g^{-1}(U) -> U is a C^\infty trivial fibration…

Study membership inference under skewed priors and adaptive thresholds, improving attack accuracy.

Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of tree-structured parameters. This paper explores an alternative notion of a tractable set, nam…

Study the structure of linear bundle morphisms between vector bundles.

Improved Frank-Wolfe method reduces dependence on data size for empirical risk minimization.

The concordance probability or C-index is a popular measure to capture the discriminatory ability of a regression model. In this article, the definition of this measure is adapted to the specific needs of the frequency and severity model, typically used during the technical pricing of a non-life insurance product. Due …

New method produces reflections with nonseparating fixed points.

Computational efficiency is an important consideration for deploying machine learning models for time series prediction in an online setting. Machine learning algorithms adjust model parameters automatically based on the data, but often require users to set additional parameters, known as hyperparameters. Hyperparamete…

The paper defines generalized s-manifolds and explores their polars and antipodal sets.

New method synthesizes data on curved spaces for better interpolation.

All projections of typical Cantor sets in high dimensions are Cantor sets.

In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these algorithms perform in "typical" scenarios, or how far the best known theoretical…

We study the concept of financial bubble in a market model endowed with a set of probability measures, typically mutually singular to each other. In this setting we introduce the notions of robust bubble and robust fundamental value in a consistent way with the existing literature in the case a unique prior exists. The…

Unified framework for clustering with sparse convex combinations.

New algorithm learns optimal policies without explicit rewards.

New findings suggest deep generative models can misclassify outliers, requiring new evaluation methods.

Extends RL to random stopping times, improving optimization.

A simple algorithm improves model generalization in expert advice settings.

It is known that all but finitely many leaves of a measured foliated 2-complex of thin type are quasi-isometric to an infinite tree with at most two topological ends. We show that if the foliation is cooriented, and the associated R-tree is self-similar, then a typical leaf has exactly one topological end. We also cons…

Inspired by work of Borzellino and Brunsden, we generalize the notion of a submanifold identifying a natural and sufficiently general condition which guarantees that a subset of an (effective) orbifold carries itself a canonical induced orbifold structure. We illustrate the strength of this approach generalizing typica…

Simple bounds for covariance and Gram matrices across various settings.

The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti and M. Mézard [Eur. Phys. B. 57, 175 (2007)]; however, they have not yet developed an approximate derivation method for fin…

Error bounds based on worst likely assignments use permutation tests to validate classifiers. Worst likely assignments can produce effective bounds even for data sets with 100 or fewer training examples. This paper introduces a statistic for use in the permutation tests of worst likely assignments that improves error b…

Let K be an algebraically closed field endowed with a complete non-archimedean norm with valuation ring R. Let f:Y -> X be a map of K-affinoid varieties. In this paper we study the analytic structure of the image f(Y) in X; such an image is a typical example of a subanalytic set. We show that the subanalytic sets are p…

New method converts p-values to e-values for more efficient CP and aggregation.

The paper challenges the belief that more inner iterations at test time improve performance in implicit deep learning.

This paper provides a set of sensitivity analysis and activity identification results for a class of convex functions with a strong geometric structure, that we coined "mirror-stratifiable". These functions are such that there is a bijection between a primal and a dual stratification of the space into partitioning sets…

Study spectral distribution of twisted Laplacian on high genus hyperbolic surfaces.

This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume t…

Study shows how missing data from certain groups can unfairly bias risk models.

Contextual bandit framework improves revenue optimization in securities lending market.

Randomly trained neural networks can generalize well if there's a simpler underlying teacher model.

Machine Learning algorithms are typically regarded as appropriate optimization schemes for minimizing risk functions that are constructed on the training set, which conveys statistical flavor to the corresponding learning problem. When the focus is shifted on perception, which is inherently interwound with time, recent…

Paper offers a method for finding the smallest sphere enclosing a set in d-dimensional space.

System states that are anomalous from the perspective of a domain expert occur frequently in some anomaly detection problems. The performance of commonly used unsupervised anomaly detection methods may suffer in that setting, because they use frequency as a proxy for anomaly. We propose a novel concept for anomaly dete…

Proposes a new Bayesian mixture of student-t processes for modeling non-stationary data.

We develop a dynamic point process model of correlated default timing in a portfolio of firms, and analyze typical default profiles in the limit as the size of the pool grows. In our model, a firm defaults at a stochastic intensity that is influenced by an idiosyncratic risk process, a systematic risk process common to…

Portfolio managers are typically constrained by turnover limits, minimum and maximum stock positions, cardinality, a target market capitalization and sometimes the need to hew to a style (such as growth or value). In addition, portfolio managers often use multifactor stock models to choose stocks based upon their respe…

Variational inference is increasingly being addressed with stochastic optimization. In this setting, the gradient's variance plays a crucial role in the optimization procedure, since high variance gradients lead to poor convergence. A popular approach used to reduce gradient's variance involves the use of control varia…

We investigate the fundamental principles that drive the development of scalable algorithms for network optimization. Despite the significant amount of work on parallel and decentralized algorithms in the optimization community, the methods that have been proposed typically rely on strict separability assumptions for o…

We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite automata. We generate a set of biased sequences by applying a finite state auto…

New rules control false discoveries in online anomaly detection for time series data.