The paper analyzes worst-case distortion risk metrics and weighted entropy under partial information.
problem Analyzing worst-case distortion risk metrics and weighted entropy with limited information.
method General distributions, partial information (mean and variance), various entropies and risk measures.
result Provides worst-case results for distortion risk metrics and weighted entropy.
The paper calculates bounds for risk metrics and entropies under partial information constraints.
problem Analyzing risk metrics and entropies for unimodal, symmetric distributions with limited information.
method Develops lower and upper bounds for worst-case distortion riskmetrics and weighted entropy for unimodal, symmetric distributions with known mean and variance.
result Sharp upper bounds for distortion riskmetrics and weighted entropy for symmetric distributions.
Sharp isoperimetric inequality on Finsler manifolds with non-negative Ricci curvature.
problem Proving an isoperimetric inequality on Finsler metric measure manifolds.
method Defining volume entropy and second Cheeger constant, proving sharp inequality.
result Sharp isoperimetric inequality involving volume entropy and weighted Ricci curvature.
We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler manifold. We prove that the convexity of all the entropies in this class is equivalent to the combination of the nonnegative weighted Ricci cur…
The paper proves lower bounds for Gaussian-weighted curvature integrals of self-shrinkers.
problem Proving lower bounds for Gaussian-weighted \(L^2\)-curvature integrals of self-shrinkers.
method Combining normal coordinate functions with weighted Poincaré inequalities and first-eigenvalue estimates.
result Explicit lower bounds in terms of entropy for closed self-shrinkers, leading to curvature gaps.
We investigate the m-relative entropy, which stems from the Bregman divergence, on weighted Riemannian and Finsler manifolds. We prove that the displacement K-convexity of the m-relative entropy is equivalent to the combination of the nonnegativity of the weighted Ricci curvature and the K-convexity of the weig…
Characterizes a new curvature bound with convexity of entropies.
problem Lowering Ricci curvature bounds with ε-range.
method Characterization through convexity of entropies over Wasserstein space.
result Derives various interpolation and functional inequalities.
New formulas derived for scalar curvature in generalized Ricci flow.
problem Scalar curvature in generalized Ricci flow.
method Derivation of weighted scalar curvature monotonicity formulas and Perelman-type energy/entropy formulas.
result New convex Nash entropies and pseudolocality principles.
New summary measures reveal geometric structure in weighted measures on manifolds.
problem Lack of geometric information in standard weight-only summaries.
method Heat-kernel entropy profiles, tracking nonuniformity across scales.
result Geometric effective sample size discounts nearby or duplicate particles.
New algorithm improves causal effect estimation for continuous treatments.
problem Observational causal inference with continuous treatments.
method End-to-end entropy balancing for maximizing causal inference accuracy.
result Our algorithm estimates causal effect more accurately than baseline.
The null energy condition is characterized via convexity of entropy in Lorentzian manifolds.
problem Characterizing the null energy condition in Lorentzian manifolds.
method Characterization via convexity of the relative entropy along displacement interpolations on null hypersurfaces.
result The null energy condition is characterized in terms of convexity of the relative entropy.
In this paper, we first introduce the weighted forward reduced volume of Ricci flow. The weighted forward reduced volume, which related to expanders of Ricci flow, is well-defined on noncompact manifolds and monotone non-increasing under Ricci flow. Moreover, we show that, just the same as the Perelman's reduced volume…
Enhances flexibility in data reweighting with optimal transport and maximum entropy principles.
problem Adapting empirical distributions to predefined constraints on moments, tail behavior, etc.
method Nonparametric distributional constraints, maximum entropy principle, optimal transport.
result Maximum entropy weight adjusted empirical distribution close to a specified distribution in optimal transport metric.
Modified Bakry-Émery criterion inequality for Tsallis entropy monotonicity.
problem Establishing improved logarithmic Sobolev inequalities and monotonicity of Tsallis entropy.
method Proving a one-parameter family of weighted Bakry-Émery Γ2 criterion inequalities and a modified inequality. result Yields a family of sharp Sobolev inequalities and monotonicity of Tsallis entropy.
Improved loss functions adapt to weight-space anisotropy, outperforming isotropic counterparts.
problem Adapting to the anisotropic nature of deep weight spaces for better performance.
method Refined local entropic loss functions restricted to a subset of weights, exploiting anisotropy.
result Partial local entropies outperform isotropic counterparts on image classification tasks.
New method estimates robust multi-period portfolios using entropy.
problem Lack of general agreement on building robust multi-period portfolios.
method Detrended cluster entropy approach to estimate portfolio weights.
result Portfolio weights are estimated reliably from real-world data at varying time horizons.
Entropy regularization is used to get improved optimization performance in reinforcement learning tasks. A common form of regularization is to maximize policy entropy to avoid premature convergence and lead to more stochastic policies for exploration through action space. However, this does not ensure exploration in th…
In the present paper, we prove that a lower bound on the 1-weighted Ricci curvature is equivalent to a convexity of entropies on the Wasserstein space. Based on such characterization, we provide some interpolation inequalities such as the Pr'ekopa-Leindler inequality, the Borel-Branscamp-Lieb inequality, and the Brun…
The paper explores inequalities for strongly-convex sets in weighted Riemannian manifolds.
problem Investigating dilation type inequalities on weighted Riemannian manifolds.
method Introducing dilation profile and comparing it with model space under lower weighted Ricci curvature bounds.
result Showed several functional inequalities related to various entropies.
Comment on entropy learning for dynamic treatment regimes.
problem Evaluating dynamic treatment regimes using entropy loss.
method Optimization-based alternative to IPW estimate.
result Suggests optimization-based approach for evaluation.
By means of a space-time Wasserstein control, we show the monotonicity of the W-entropy functional in time along heat flows on possibly singular metric measure spaces with non-negative Ricci curvature and a finite upper bound of dimension in an appropriate sense. The associated rigidity result on the rate of dissipatio…
MEC-Cox: A Machine-Learning-Assisted Generalized Entropy Calibration Method for Estimating ATT Marginal Hazard-Ratio
problem Estimating ATT marginal hazard-ratio in externally controlled survival trials
method Machine-learning-assisted generalized entropy calibration for IPW Cox regression
result Reduces bias, increases efficiency, and improves coverage
This paper presents a new fuzzy k-means algorithm for the clustering of high-dimensional data in various subspaces. Since high-dimensional data, some features might be irrelevant and relevant but may have different significance in the clustering process. For better clustering, it is crucial to incorporate the contribut…
Establishes Yau-Tian-Donaldson conjecture for weighted metrics.
problem Constant scalar curvature Kähler metrics on polarized projective manifolds.
method Extends Chi Li's work to weighted case, uses a priori estimates and slope formulas.
result Proves Yau-Tian-Donaldson conjecture for weighted extremal Kähler metrics.
DAC enhances exploration in reinforcement learning with entropy regularization.
problem Improving exploration efficiency in reinforcement learning.
method Sample-aware entropy regularization using replay buffer action distributions.
result DAC significantly outperforms existing algorithms in reinforcement learning tasks.
New surface area measures defined for ball-convex bodies, leading to entropy and inequalities.
problem Defining and analyzing surface area measures for ball-convex bodies.
method Introducing Lp relative surface areas, proving invariance and inequalities, and using geometric interpretations. result Established inequalities and a new notion of entropy for ball-convex bodies.
We examine a class of deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical physics methods, under the assumption that weight matrices are independent and ort…
This paper reformulates Fβ for better model performance and interpretation.
problem Optimizing model performance and interpretation using Fβ metric. method Reformulate Fβ metric to facilitate statistical distributions and dynamic penalty weights. result Better and interpretable results with a 14% boost in F1 score for IMDB data. In the article, we generalize some recent results of Colding and Minicozzi on generic singularities of mean curvature flow to curved ambient spaces. To do so, we make use of a weighted monotonicity formula to derive an "almost monotonicity" for the entropy upon embedding into Rℓ. We are also lead to study the co…
At the core of any inference procedure in deep neural networks are dot product operations, which are the component that require the highest computational resources. A common approach to reduce the cost of inference is to reduce its memory complexity by lowering the entropy of the weight matrices of the neural network, …
Study shows only grim reaper cylinder for certain self-translating surfaces.
problem Characterizing self-translating surfaces in 3D space.
method Used parabolicity in a weighted setting and universally L-superharmonic functions.
result Characterized the grim reaper cylinder as the only finite entropy self-translating 2-surface in R^3 of width π and bounded from below.
The paper studies entropy of harmonic metrics on cyclic Higgs bundles.
problem Quantifying the degree of mutual misalignment of Hermitian metrics.
method Introduces entropy function and estimates its bounds for cyclic Higgs bundles.
result Entropy difference converges to a finite real number for β>−1. IWeS selects examples by entropy-based importance sampling for subset selection.
problem Efficiently selecting examples for model training in batch settings.
method IWeS uses importance sampling based on model entropy to select examples.
result IWeS outperforms other subset selection algorithms on seven datasets.
We derive weighted log-Sobolev inequalities from a class of super Poincaré inequalities. As an application, the Talagrand inequality with larger distances are obtained. In particular, on a complete connected Riemannian manifold, we prove that the $\log^\dd$-Sobolev inequality with $\dd\in (1,2)$ implies the $L^{2/(2-\d…
Enhances RL by controlling policy stochasticity through trajectory entropy constraints.
problem Non-stationary Q-value estimation and short-sighted entropy tuning in maximum entropy RL.
method Proposes TECRL framework with separate Q-functions for reward and entropy, enforcing a trajectory entropy constraint.
result DSAC-E algorithm achieves higher returns and better stability on OpenAI Gym benchmarks.
A new method for feature fusion in U-Net decoders using difference-based gating.
problem Precise fusion of high-level semantics and low-level details in U-Net decoder reconstruction.
method Proposes two difference-based gating approaches: Feature-difference gating (FDG) and Entropy-difference gating (EDG).
result Both FDG and EDG methods outperform existing attention-based fusion methods, with EDG showing superior performance.
JES optimizes expensive functions by considering joint entropy over input and output spaces.
problem Optimizing expensive functions with limited evaluations.
method Joint Entropy Search (JES) considers joint entropy over input and output spaces.
result JES outperforms other information-theoretic methods in Bayesian optimization.
The paper extends entropy concepts to Monge-Ampère measures with prescribed singularities.
problem Investigating entropy for Monge-Ampère measures with specific singularities.
method Generalizing entropy for potentials, studying stability under blow-ups and perturbations, proving Moser-Trudinger inequalities.
result Functions with finite entropy belong to a specific energy class and maintain singularities of the model potential.
New analysis shows how cross-entropy training shapes attention in transformers.
problem Understanding how gradient-based learning creates the required internal geometry in transformers.
method Developed a first-order analysis of cross-entropy training effects on attention scores and values in a transformer attention head.
result Introduced an advantage-based routing law and responsibility-weighted update for attention scores and values, respectively.
We introduce a pathwise approach to analyze the relative performance of an equity portfolio with respect to a benchmark market portfolio. In this energy-entropy framework, the relative performance is decomposed into three components: a volatility term, a relative entropy term measuring the distance between the portfoli…
In this paper, we present a novel and general framework called {\it Maximum Entropy Discrimination Markov Networks} (MaxEnDNet), which integrates the max-margin structured learning and Bayesian-style estimation and combines and extends their merits. Major innovations of this model include: 1) It generalizes the extant …
Attention to entropic communication improves message decoding and cooperation.
problem Improper weighting in attention mechanisms hinders optimal communication.
method Combining attention and relative entropy (RE) for optimal message encoding and decoding.
result Proper attention communication emerges via weighted RE, aiding optimal protocols.
New loss function restores importance weighting in overparameterized models.
problem Restoring importance weighting in overparameterized neural networks.
method Introduced polynomially-tailed losses to restore effects of importance weighting.
result Polynomially-tailed losses improve performance in correcting distribution shift.
The effect of proportional transaction costs on systematically generated portfolios is studied empirically. The performance of several portfolios (the index tracking portfolio, the equally-weighted portfolio, the entropy-weighted portfolio, and the diversity-weighted portfolio) in the presence of dividends and transact…
AECF improves multimodal inference robustness and calibration.
problem Robustness and calibration issues in multimodal systems with missing inputs.
method Adaptive Entropy-Gated Contrastive Fusion (AECF) layer.
result Improves masked-input mAP by +18 pp at a 50% drop rate.
This paper proposes a new method for efficient data compression using Bayesian neural networks.
problem Efficient compression of data represented as functions mapping coordinates to signal values.
method Overfitting variational Bayesian neural networks to the data and compressing an approximate posterior weight sample using relative entropy coding.
result Our method achieves strong performance on image and audio compression while retaining simplicity.
PLD distills knowledge using choice-theoretic Plackett-Luce model.
problem Model compression and knowledge transfer between large and small networks.
method PLD uses a weighted list-wise ranking loss based on the Plackett-Luce model.
result PLD achieves consistent gains across diverse architectures and distillation methods.
The paper tackles efficient exploration in MDPs to learn accurate models.
problem Efficient exploration in MDPs to learn accurate models.
method Formalizes the problem, introduces an algorithm for ε-accurate model estimation, and proposes a heuristic-based algorithm. result Heuristic-based algorithm outperforms original algorithm in small sample regime.