We simplify information measure computation using learned features.
problem Computing information measures from raw data is computationally expensive.
method Developed a separable design for computing information measures from learned feature representations.
result A variety of information measures can be computed efficiently through learned feature representations.
Researchers compute the ratio between two normalizations of Thurston measure on measured laminations.
problem Computing the ratio between two normalizations of Thurston measure.
method Using the integral and symplectic structures on the space of measured laminations.
result Computed the ratio between two normalizations of Thurston measure.
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these measures satisfy all the Granger's axioms for an "ideal measure". One such ideal…
Quantum machine learning tackles large datasets with randomized measurements.
problem Efficiently process large, high-dimensional datasets on quantum computers.
method Randomized measurements to scale linearly with dataset size and quadratic for post-processing.
result Substantial speed-up for noisy quantum computers, enabling image classification.
FPI methods compute barycenters of Gaussian sets for various dissimilarity measures.
problem Efficiently compute barycenters of Gaussian sets for multiple dissimilarity measures.
method Fixed-Point Iterations (FPI) for several dissimilarity measures.
result FPI provides a useful toolbox for fusion/reduction of Gaussian sets.
A novel approach to computing barycenters on graph-supported probability measures.
problem Computing weighted averages of measures on graphs.
method Dynamic optimal transport formulation on the simplex, gradient descent on the probability simplex.
result Intrinsic gradient descent provides a coherent framework for synthesizing and analyzing measures on graphs.
Study on identifying probability distributions from random data, showing computable partial learners exist.
problem Identifying probability distributions from random data samples.
method Algorithmic learning theory approach, focusing on computable probability measures and high oracles.
result Characterization of oracles that compute explanatory learners for computable probability measures.
New multivariate risk measures improve on univariate OCE methods.
problem Improving risk assessment in multivariate settings.
method Inspired by univariate OCE, introduces convex, monotonic, cash-invariant measures.
result Numerical algorithms provide error estimates for computations.
Paper presents a new VMBQC model with fewer parameters for better generative modeling.
problem Limited generative power of VMBQC due to more parameters than unitary models.
method Introduces a restricted VMBQC model with a single additional trainable parameter.
result Minimal extension of VMBQC model generates distributions not learnable by unitary models.
We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of sequences may be singled out almost surely with respect to certain probability …
Paper uses neural networks to efficiently compute vertex centrality measures in large networks.
problem Efficiently computing vertex centrality measures in massive real-world networks.
method Neural network learning algorithms to approximate centrality measures.
result Neural network regression model outperforms other techniques in terms of solution quality and computation time.
A scalable approach to learning from probability measures using quantization.
problem Efficiently comparing and manipulating large sets of probability measures.
method Quantization of probability measures to a fixed support, followed by optimal transport computations.
result Consistency and convergence guarantees for quantized measures in various OT-based tasks.
The paper introduces a new method for risk measurement using weak optimal transport.
problem Risk measurement in insurance and financial contexts.
method Convex risk measures with weak optimal transport penalties, explicit representation via nonlinear transform, computational aspects, and approximations using neural networks.
result Explicit representation and computational methods for risk measures.
Enhances SGLD for log-concave posteriors with asynchronous computation.
problem Sampling log-concave posterior distributions efficiently.
method Integrates asynchronous computation into SGLD with delayed gradients.
result Convergence in measure is not significantly affected by delayed gradient information.
Quadratic-time algorithm computes stretch factors and foliations for pseudo-Anosov mapping classes.
problem Computing stretch factors and foliations for pseudo-Anosov mapping classes efficiently.
method Quadratic-time algorithm using input word and length as complexity measure.
result First algorithm to compute stretch factors and foliations in sub-exponential time.
Deep kernel learning for complex function modeling.
problem Modeling complex functions with line integral measurements.
method Gaussian process with neural networks for line integral data.
result Improved performance in computed tomography reconstruction.
A neural network speeds up computation of Wasserstein barycenters by 60x.
problem Computing Wasserstein barycenters is computationally demanding.
method Trained a deep convolutional neural network to compute Wasserstein barycenters.
result Computational times reduced from milliseconds to seconds.
We extend Sobolev transport to unbalanced measures on graphs.
problem Optimal transport struggles with measures of different total mass and high computational complexity.
method We propose a scalable unbalanced Sobolev transport (UST) for measures on graphs.
result UST admits a closed-form formula for fast computation and is negative definite.
MBQC linked to CQCA, yielding efficient Ansätze.
problem Quantum computation efficiency and Ansatz adaptation.
method Relating MBQC to CQCA and constructing Ansätze.
result MBQC Ansätze can lead to different performances on learning tasks.
AI progress measured by reduced compute needed to reach past performance.
problem Quantifying algorithmic progress in AI.
method Analysis of floating-point operations required to train neural networks.
result Algorithmic efficiency doubled every 16 months over 7 years.
This paper introduces Hausdorff measure and its applications in fractal geometry.
problem Defining and applying Hausdorff measure to fractal geometry.
method Definition of Hausdorff outer measure, Caratheodory's criterion, construction of Hausdorff measure, and introduction of Hausdorff dimension.
result Demonstrates the Hausdorff dimension of the Cantor ternary set.
New measure defined on surface strata, invariant under scaling.
problem Defining an invariant measure on moduli spaces of dilation surfaces.
method Novel computation of cohomology with coefficients for mapping class group.
result SL(2,R)-invariant Lebesgue class measure on strata.
Mixed-integer programming solves systemic risk measures for interdependent financial systems.
problem Computing systemic risk measures for interdependent financial systems with joint risk considerations.
method Proposes a mixed-integer programming problem to compute clearing vectors in a Rogers-Veraart network model with unrestricted sign operating cash flows.
result The proposed mixed-integer programming problem can compute systemic risk measures for interdependent financial systems.
We consider the class of risk measures associated with optimized certainty equivalents. This class includes several popular examples, such as CV@R and monotone mean-variance. Numerical schemes are developed for the computation of these risk measures using Fourier transform methods. This leads, in particular, to a very …
Proposes methods to compute optimal transport maps via subspace projections.
problem Computing optimal transport in high dimensions is challenging due to the curse of dimensionality.
method Develops two methods to extrapolate optimal transport plans from subspace projections to the full space.
result The best optimal transport plan is a generalization of the Knothe-Rosenblatt transport.
Study exact polynomials to compute Mahler measure and relate it to volume function.
problem Compute Mahler measure of exact polynomials.
method Define volume function on vanishing set, prove local extrema on 2D torus, derive Mahler measure formula.
result Prove Mahler measure of irreducible exact polynomials is greater than volume function amplitude.
Paper proposes data quality measures for large-scale high-dimensional data.
problem Lack of practical data quality measures for large-scale high-dimensional data.
method Proposes two data quality measures: class separability and in-class variability. Efficient algorithms based on random projections and bootstrapping are provided.
result Efficient algorithms for computing data quality measures on large-scale high-dimensional data.
New MBQC algorithm uses randomness for generative modeling.
problem Designing efficient quantum algorithms for generative modeling.
method Proposes a variational MBQC algorithm that treats randomness as a resource.
result Randomness in MBQC can lead to significant gains in generative modeling performance.
Novel algorithm speeds up computation of Sobolev IPM for graph-based probability measures.
problem Efficient computation of Sobolev IPM for graph-based probability measures.
method Established relation between Sobolev norm and weighted Lp-norm, proposed novel regularization, leveraged graph structure. result Proposed regularized Sobolev IPM provides closed-form expression for fast computation.
Measure homology was introduced by Thurston in his notes about the geometry and topology of 3-manifolds, where it was exploited in the computation of the simplicial volume of hyperbolic manifolds. Zastrow and Hansen independently proved that there exists a canonical isomorphism between measure homology and singular hom…
The paper proposes a new framework for accurate uncertainty representation and propagation.
problem Inaccurate representation and propagation of uncertainty in measurement systems.
method The paper introduces a comprehensive framework using Gaussian Mixture Models (GMMs) for representing and propagating quantitative attributes in measurement systems.
result GMMs offer improved accuracy in representing and propagating measurement uncertainty compared to traditional Gaussian methods, while maintaining computational tractability.
Proves Vol-Det Conjecture for many alternating links using Mahler measures.
problem Vol-Det Conjecture relating hyperbolic link volumes and determinants.
method Exact computations of Mahler measures of two-variable polynomials.
result Proves Vol-Det Conjecture for many infinite families of alternating links.
Improved computational efficiency for estimating Wasserstein distance.
problem Inefficient computation of Wasserstein distance for large samples.
method Developed Sample-Sketch-Solve paradigm using grid sketches.
result Approximates Wasserstein distance within ε error in ε^(-max(2, (d+1+o(1))/(1+α))) time.
A hybrid impurity measure balances theoretical soundness and computational efficiency.
problem Developing a robust impurity measure for decision trees.
method Integrates Tsallis entropy with an exponential polarization component.
result Simple parametric measures outperform ITC, but ITC variants are competitive with strong theoretical guarantees.
Proposes robust ABC method for outlier detection.
problem Outliers sensitivity in ABC methods.
method γ-divergence estimator with redescending property.
result Significantly higher robustness than existing methods.
Efficiently computes optimal policies for Entropic Risk Measures.
problem Optimizing risk-sensitive metrics in MDPs is computationally expensive.
method Uses Entropic Risk Measures and novel structural analysis for efficient computation.
result Achieves strong performance in various decision-making scenarios.
Proposes a computational framework for real-time risk assessment and prioritization.
problem Real-time risk assessment and prioritization for uncertain outcomes.
method Develops a computational framework based on satisficing measure for real-time risk assessment and prioritization. Applies sample average approximation and primal-dual stochastic approximation algorithms.
result Demonstrates the effectiveness of the proposed framework in real-time risk assessment and prioritization.
This paper develops efficient bounds on the Wasserstein metric for discrete measures.
problem Computing the exact Wasserstein metric is computationally expensive.
method Formulates and solves a Kantorovich problem on a coarse grid using quantized measures and cost matrices, followed by upscaling and correction.
result Achieves a 10x-100x speedup while maintaining low approximation error.
Measure homology was introduced by Thurston in order to compute the simplicial volume of hyperbolic manifolds. Berlanga endowed measure homology with a structure of graded locally convex (possibly non-Hausdorff) topological vector space. In this note we completely characterize Berlanga's topology on measure homology of…
A new measure helps compute suboptimality in entropy-regularized methods.
problem Computing suboptimality in entropy-regularized variational objectives when unnormalised densities are unavailable.
method Introduced 'kernel gradient discrepancy' (KGD) to compute suboptimality explicitly.
result KGD characterizes kernel Stein discrepancy (KSD) in the standard Bayesian context and measures variational gradient size.
Computer graphics techniques improve art pricing by measuring painting effort.
problem Traditional art pricing models lack measures for conceptual and painting efforts.
method Applied image recognition to measure line and color variances as proxies for effort.
result Painting effort (line and color variances) significantly positively correlates with sales price.
Different approaches to defining dynamic market risk measures are available in the literature. Most are focused or derived from probability theory, economic behavior or dynamic programming. Here, we propose an approach to define and implement dynamic market risk measures based on recursion and state economy representat…
The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of clearing houses. The two main issues in systemic risk measurement are the compu…
Parallel algorithm speeds up Jones polynomial computation.
problem Efficient computation of knot complexity measures.
method First parallel algorithm for exact Jones polynomial computation.
result Reduces computational time by an exponential factor.
A new metric for comparing probability measures on graphs, scalable and negative definite.
problem Optimal transport's high complexity and indefiniteness for kernel machines.
method Sobolev transport metric for graph metrics, closed-form formula, negative definiteness.
result Sobolev transport yields a scalable and negative definite metric.
Sliced Optimal Transport simplifies OT for fast computation.
problem Efficient computation of distances and barycenters for probability measures.
method Combines OT, integral geometry, and statistics for fast computation.
result Retains rich geometric structure while speeding up computations.
This paper extends financial theory to measure learnable market structure under computational constraints.
problem Understanding learnable market structure under bounded computational capacity.
method Introduces financial epiplexity as a measure of learnable market structure, extending classical information theory.
result Proves that equal entropy does not imply equal epiplexity and derives thresholds for useful regimes.
AI measures financial risk using linear quantile lasso regression.
problem Measuring systemic financial risk accurately and quantitatively.
method Linear quantile lasso regression with penalization parameter lambda.
result The Financial Risk Meter (FRM) is a valid measure of systemic risk.