The cost of holding a suboptimal portfolio instead of the Kelly-optimal one admits two exact relative-entropy representations. Under the true measure, the expected log-wealth shortfall equals the KL d...
Complex structures often emerge from initially homogeneous or weakly correlated states. We address the apparent tension between this ordering and entropy growth through a unified framework combining s...
We study risk-neutral density extraction from short-dated option chains. As expiry approaches, option premia decline and bid--ask spreads can be large relative to prices, making mid quotes particularl...
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probab...
Decentralized Federated Learning (DFL) remains highly vulnerable to adaptive backdoor attacks designed to bypass traditional passive defense metrics. To address this limitation, we shift the defensive...
Extreme economic outcomes are not shaped by tails alone. They are also shaped by unequal access to opportunities. This paper develops a theory of heterogeneous extremes by taking the distribution of o...
Efficient exploration is a central problem in reinforcement learning and is often formalized as maximizing the entropy of the state-action occupancy measure. While unconstrained maximum-entropy explor...
This study investigates whether the macroscopic statistical maturity of cryptocurrencies implies dynamical equivalence with traditional equity markets. We analyze high-frequency data (2020--2025) usin...
Modeling the dynamics of non-stationary stochastic systems requires balancing the representational power of deep learning with the mathematical transparency of classical models. While classical Markov...
Comparing two probability distributions is a basic building block of statistics and machine learning, and the right family is well understood: the Rényi divergences of order $α\in[0,\infty]$ are the u...
We consider predictive density estimation under logarithmic score for $d$-dimensional infinitely divisible location models. Taking the formal Bayes predictive density under the Lebesgue prior as a ben...
Group Relative Policy Optimization (GRPO) has emerged as the de facto Reinforcement Learning (RL) objective driving recent advancements in Multimodal Large Language Models. However, extending this suc...
Test-Time Reinforcement Learning (TTRL) enables Large Language Models (LLMs) to enhance reasoning capabilities on unlabeled test streams by deriving pseudo-rewards from majority voting consensus. Howe...
Recent vision-language models (VLMs) typically rely on a single vision encoder trained with contrastive image-text objectives, such as CLIP-style pretraining. While contrastive encoders are effective ...
In generalized extreme value model for the r largest order statistics, denoted by rGEV, the selection of r is critical. The existing entropy difference test for selecting r is applicable to large samp...
The vast collection of machine learning records available on the web presents a significant opportunity for meta-learning, where past experiments are leveraged to improve performance. Two crucial meta...
Most unified large multimodal models (LMMs) that support both visual understanding and image generation still rely on curated post-training supervision, such as human annotations, preference labels, o...
We develop an efficient online algorithm to sample a sequence of discrete random variables using an entropy source of i.i.d. fair coin flips, in a standard model of real computation where real-valued ...
A Bayesian investor learns an unknown asset drift by Kalman-Bucy filtering and trades the mean-variance optimal portfolio, but his observation model may be wrong. We make the policy robust to an adver...
This paper considers nonparametric regression from strongly mixing observations. The proposed approach is based on deep neural networks with minimum error entropy (MEE) principle. We study two estimat...
🌊
