A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study on risk measures using distorted Choquet integrals with random distortions.
New method tests risk measures for various distortions.
ReLU networks don't exponentially distort curve lengths as previously thought.
New bounds for optimal transport using Gaussian processes and rate-distortion functions.
We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The second, simultaneously applies the distortion on the survival function of the su…
Paper proposes robust risk measures for non-negative risks with partial information.
New insights into image compression trade-offs with private randomness.
Researchers prove inner product recovery is impossible in latent space models.
We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A more fundamental problem when extending the distorted expectation to a dynamic se…
New concept of partial comonotonicity connects riskmetrics and dependence.
U-Net trained to recover acoustic interference striations from distorted data.
Establishes a link between risk measures and uniform integrability in finance.
Random projections have been applied in many machine learning algorithms. However, whether margin is preserved after random projection is non-trivial and not well studied. In this paper we analyse margin distortion after random projection, and give the conditions of margin preservation for binary classification problem…
In cognitive psychology, automatic and self-reinforcing irrational thought patterns are known as cognitive distortions. Left unchecked, patients exhibiting these types of thoughts can become stuck in negative feedback loops of unhealthy thinking, leading to inaccurate perceptions of reality commonly associated with anx…
Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on how many projections are needed to accurately preserve the geometry of these man…
A new distortion measure optimizes function approximations in vector quantization.
We study a new class of codes for lossy compression with the squared-error distortion criterion, designed using the statistical framework of high-dimensional linear regression. Codewords are linear combinations of subsets of columns of a design matrix. Called a Sparse Superposition or Sparse Regression codebook, this s…
In this paper, we introduce the rich classes of conditional distortion (CoD) risk measures and distortion risk contribution (CoD) measures as measures of systemic risk and analyze their properties and representations. The classes include the well-known conditional Value-at-Risk, conditional Expected Shortfall, and r…
Introduces joint exclusivity (JE), a new form of negative dependence.
We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the choice of an appropriate epoch over which the empirical cross-correlation return ma…
FMix improves model performance by distorting learned functions without distorting data distribution.
MLDL preserves manifold geometry in vector transformations.
Study evaluates methods for expanding communities in hypergraphs using random walks.
Vertex distortion detects if a knot is unknot.
The Whitney embedding theorem gives an upper bound on the smallest embedding dimension of a manifold. If a data set lies on a manifold, a random projection into this reduced dimension will retain the manifold structure. Here we present an algorithm to find a projection that distorts the data as little as possible.
New method corrects complex distortions in single view images.
The paper studies how norms of random vectors are preserved by random projections.
Algorithm finds optimal affine transformation to minimize overall distortion.
We propose a data-driven framework for optimizing privacy-preserving data release mechanisms to attain the information-theoretically optimal tradeoff between minimizing distortion of useful data and concealing specific sensitive information. Our approach employs adversarially-trained neural networks to implement random…
Vertex distortion measures how far lattice knots deviate from straight lines.
The standard margin-based structured prediction commonly uses a maximum loss over all possible structured outputs. The large-margin formulation including latent variables not only results in a non-convex formulation but also increases the search space by a factor of the size of the latent space. Recent work has propose…
We consider the problem of distortion minimal morphing of -dimensional compact connected oriented smooth manifolds without boundary embedded in . Distortion involves bending and stretching. In this paper, minimal distortion (with respect to stretching) is defined as the infinitesimal relative change in vol…
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure. The proposed method creates random clique adjacency matrices for each k-skeleton…
QC-SPHARM detects Alzheimer's Disease early using hippocampal surface geometry.
This paper shows how to calculate risk measures for sums of two counter-monotonic risks.
Study distortion risk measures for step-weighted distributions.
The distortion of a curve measures the maximum arc/chord length ratio. Gromov showed any closed curve has distortion at least pi/2 and asked about the distortion of knots. Here, we prove that any nontrivial tame knot has distortion at least 5pi/3; examples show that distortion under 7.16 suffices to build a trefoil kno…
In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be computed in log-linear time, providing efficient dimensionality reduction of gene…
Computed distortion coefficients for the α-Grushin plane.
We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a …
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire, continuous, open and discrete mapping of finite distortion which is piecewise smooth, ha…
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear…
Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performances, these methods are supported by a well-developed theory. Kernel methods use an implicit mapping of the input data into a high dimensional f…
The distortion of a curve is the supremum, taken over distinct pairs of points of the curve, of the ratio of arclength to spatial distance between the points. Gromov asked in 1981 whether a curve in every knot type can be constructed with distortion less than a universal constant C. Answering Gromov's question seems to…
The study shows exponential distortion in virtually special groups containing free subgroups.
Estimates rate-distortion function for large datasets using neural networks.
New coding theorem shows achievable rate matches theoretical limit.
We construct 2-dimensional CAT(-1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential.