Extends DP-means to handle outliers in f-separable distortion measures.
problem Vulnerability to outliers and large maximum distortion in clusters.
method Extends DP-means to f-separable distortion measures and proposes a robust learning algorithm. result Demonstrates improved performance in handling outliers and reducing maximum distortion.
Vertex distortion detects if a knot is unknot.
problem Determining if a knot is the unknot.
method Using Denne-Sullivan's bound on Gromov distortion, the vertex distortion of nontrivial lattice knots is bounded. Then, it is shown that trivial vertex distortion implies the unknot.
result The conjecture that trivial vertex distortion implies the unknot is proven.
Let F be an incompressible, meridionally incompressible and not boundary-parallel surface with boundary in the complement of an algebraic tangle (B,T). Then F separates the strings of T in B and the boundary slope of F is uniquely determined by (B,T) and hence we can define the slope of the algebraic tang…
New method corrects complex distortions in single view images.
problem Complex distortions in images, especially those caused by refractive surfaces.
method Differentiable image sampling and semantic information augmentation.
result Model can estimate and correct highly complex distortions.
Algorithm finds optimal affine transformation to minimize overall distortion.
problem Minimizing distortion in affine transformations.
method Riemannian geometry approach to define and minimize distortion.
result Mean distorting transformation found for minimizing overall distortion.
Vertex distortion measures how far lattice knots deviate from straight lines.
problem Measuring how much lattice knots deviate from straight paths.
method Analogous to smooth knots, study vertex distortion in lattice knots.
result Vertex distortion is 1 only for the unknot and can be arbitrarily high.
We consider the problem of distortion minimal morphing of n-dimensional compact connected oriented smooth manifolds without boundary embedded in Rn+1. Distortion involves bending and stretching. In this paper, minimal distortion (with respect to stretching) is defined as the infinitesimal relative change in vol…
This paper shows how to calculate risk measures for sums of two counter-monotonic risks.
problem Calculating risk measures for sums of two counter-monotonic risks.
method Using a fixed distortion function and expressing the risk measure of a sum as the sum of two related measures of the marginals.
result The risk measure of a sum of two counter-monotonic risks can be expressed as the sum of two related distortion risk measures of the marginals.
A new family of stochastic dominance orders based on distortion functions.
problem Determining a continuum of dominance relations for risk assessment.
method Introducing H-distorted stochastic dominance, a generalized family of stochastic orders.
result Power-distorted stochastic dominance is particularly appealing due to its simplicity and statistical interpretations.
Study distortion risk measures for step-weighted distributions.
problem Analyzing risk measures for specific distribution types.
method Investigate distortion risk measures of step-weighted distributions.
result Developed methods for calculating risk measures.
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…
The paper calculates subgroup distortions in 3-manifold groups.
problem Understanding subgroup distortions in 3-manifold groups.
method Computed all finitely generated subgroups of finitely generated 3-manifold groups and analyzed their distortions.
result Subgroup distortions in 3-manifold groups are linear, quadratic, exponential, or double exponential.
Computed distortion coefficients for the α-Grushin plane.
problem Analyzing the distortion coefficients of the α-Grushin plane.
method Using generalised trigonometric functions and synthetic curvature conditions.
result Estimates for distortion coefficients and a curvature condition conjecture.
Study on risk measures using distorted Choquet integrals with random distortions.
problem Developing risk measures under random distortions of capacities.
method Introducing and analyzing randomly distorted Choquet integrals with respect to a distorted capacity, establishing properties and providing representations.
result Representation of comonotonic additive conditional risk measures using G-randomly distorted Choquet integrals.
Sharp bounds on distortion of surfaces in 3D space.
problem Finding the minimum distortion of surfaces in 3D space.
method Analyzing convex embedded 2-spheres and surfaces of positive genus.
result π/2 is a sharp lower bound on the distortion of surfaces of positive genus.
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…
New study shows tradeoffs between compression quality, distortion, and perception.
problem Optimizing compression for low distortion often sacrifices perceptual quality.
method Adopted Blau & Michaeli's perceptual quality definition and studied the rate-distortion-perception tradeoff.
result Restricting perceptual quality to high generally requires a trade-off between rate and distortion.
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.
problem Understanding distortion in virtually special groups containing free subgroups.
method Constructing examples of virtually special groups with finite rank free subgroups.
result Distortion functions grow like exp^k(x^m) and can be superexponential.
Estimates rate-distortion function for large datasets using neural networks.
problem Designing lossy data compression schemes and comparing them with theoretical limits.
method Re-formulate rate-distortion objective and solve using neural networks.
result NERD accurately estimates the rate-distortion function for real-world datasets.
Introduces new performance criteria for investment under distorted probabilities.
problem Reconciling time-consistent performance with probability distortions.
method Two definitions of forward rank-dependent criteria, equivalence established; characterization of viable probability distortion processes.
result Characterization of optimal wealth process and new distorted measure.
Study stabilizers in handlebody group; meridians are undistorted, others are exponentially distorted.
problem Geometric properties of stabilizers in handlebody group.
method Analysis of stabilizers of meridians and primitive curves/annuli.
result Stabilizers of meridians are undistorted, others are exponentially distorted.
New coding theorem shows achievable rate matches theoretical limit.
problem Unknown existence of encoders and decoders for RDPF.
method Used stochastic, variable-length codes to prove RDPF achievable.
result Achievable rate matches theoretical rate-distortion-perception function.
We construct 2-dimensional CAT(-1) groups which contain free subgroups with arbitrary iterated exponential distortion, and with distortion higher than any iterated exponential.
Paper proposes a new black-box attack approach to minimize visual distortion.
problem Constructing adversarial examples that minimize visual distortion in a black-box threat model.
method Learning the noise distribution of adversarial examples to approximate the gradient of a non-differentiable loss function.
result The proposed attack results in much lower visual distortion compared to state-of-the-art black-box attacks.
Sharp bounds for distortion risk metrics under uncertain distributions.
problem Modeling risk metrics under distributional uncertainty.
method Established bounds for distortion risk metrics using specific features of underlying distributions.
result Identified worst- and best-case values of distortion risk metrics.
Study dynamic risk measures and performance indices using distortion functions.
problem Investigate time consistency of dynamic risk measures and performance indices generated by distortion functions.
method Analyze dynamic coherent risk measures (DCRMs) and dynamic weighted value at risk measures, proving their equivalence. Establish properties of families of DCRMs generated by distortion functions and define corresponding dynamic coherent acceptability indices (DCAIs). Examine time consistency of DCRMs and DCAIs.
result DCRM generated by distortion functions are sub-martingale time consistent but not super-martingale time consistent and not weakly acceptance time consistent.
New bounds on knot distortion and Seifert surface properties.
problem Understanding the distortion of knots and properties of Seifert surfaces.
method Analyzing embeddings of Seifert surfaces and using properties of monodromy maps.
result Bounds on the distortion of certain knots and properties of Seifert surfaces.
The problem behind this paper is the proper measurement of the degree of quality/acceptability/distance to arbitrage of trades. We are narrowing the class of coherent acceptability indices introduced by Cherny and Madan (2007) by imposing an additional mathematical property. For this, we introduce the notion of a conca…
New method tests risk measures for various distortions.
problem Testing risk measures for different distortions.
method Stratification and randomization of risk levels.
result Method performs well in numerical case studies.
We study the statistical meaning of the minimization of distortion measure and the relation between the equilibrium points of the SOM algorithm and the minima of distortion measure. If we assume that the observations and the map lie in an compact Euclidean space, we prove the strong consistency of the map which almost …
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…
We discuss equivalent axiomatic characterizations of distortion risk measures, and give a novel and concise proof of the characterization of elicitable distortion risk measures. Elicitability has recently been discussed as a desirable criterion for risk measures, motivated by statistical considerations of forecasting. …
Machine learning detects and classifies cognitive distortions in mental health texts.
problem Detect and classify cognitive distortions in mental health texts to improve treatment.
method Machine learning framework using crowdsourced and therapy dataset.
result Model achieved high F1 scores for detecting and classifying cognitive distortions.
Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on fi…
New method optimizes lossy compression models more effectively.
problem Difficulty in manually setting a tradeoff parameter for lossy compression models.
method Constrained optimization method of Rezende and Viola, 2018.
result The method enables pointwise model comparisons and outperforms existing methods.
New examples of distorted interval diffeomorphisms found.
problem Finding C2-undistorted C1+α-distorted diffeomorphisms of the interval. method Explicit computations and failure of a classical lemma extension.
result First examples of C2-undistorted C1+α-distorted diffeomorphisms. ReLU networks don't exponentially distort curve lengths as previously thought.
problem Understanding how neural networks distort curve lengths with depth.
method Analyzing expected length distortion of ReLU networks with random initialization.
result Expected length distortion does not grow with depth, and shrinks slightly.
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 studies fundamental limits of communication in distributed learning.
problem Communication efficiency in model aggregation for distributed learning.
method Rate-Distortion approach to model aggregation as a vector Gaussian CEO problem.
result Derives rate region bound and sum-rate-distortion function for model aggregation.
Paper introduces new risk measures that unify two existing types.
problem Combining two types of risk measures for broader applicability.
method Introduces a new class of risk measures that unify distortion and Haezendonck-Goovaerts measures.
result New risk measures defined on a larger space, with coherent properties in certain scenarios.
Let S be an immersed horizontal surface in a 3-dimensional graph manifold. We show that the fundamental group of the surface S is quadratically distorted whenever the surface is virtually embedded (i.e., separable) and is exponentially distorted when the surface is not virtually embedded.
A CNN method removes atmospheric distortion from video sequences.
problem Mitigating atmospheric distortion in video sequences.
method End-to-end supervised convolutional neural network (CNN) with residual learning.
result The method outperforms existing techniques in terms of image quality and speed.
Optimizes communication in federated learning using rate-distortion theory.
problem Reduces communication cost in federated learning while maintaining model accuracy.
method Applies rate-distortion theory to model updates, proposing distortion as a proxy for accuracy.
result Near-optimal communication reduction, outperforming other methods on a FL benchmark.
Paper derives best- and worst-case GlueVaR measures with incomplete data.
problem Risk measurement with limited information and shape constraints.
method Unified framework based on partial distribution information and shape properties.
result Characterization of extremal GlueVaR distributions with convex envelopes.
Our main result is a nontrivial lower bound for the distortion of some specific knots. In particular, we show that the distortion of the torus knot Tp,q satisfies δ(Tp,q)>1601min(p,q). This answers a 1983 question of Gromov.
New adversarial examples with structured distortion sets improve robustness and perceptibility.
problem Improving adversarial robustness and perceptibility of images.
method Exploring and constraining adversarial search with trace-norms and other norms.
result Structured adversarial perturbations allow larger distortions and control over generation.
Paper proposes a method to make image model explanations robust to distortions.
problem Ensuring robustness of explanations for images under distortions.
method Embedding perceptual distances in surrogate explainers to evaluate and improve robustness.
result Surrogate explanations become more coherent and robust to distortions.