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.
Modified Bakry-Émery criterion inequality for Tsallis entropy monotonicity.
The construction of efficient and effective decision trees remains a key topic in machine learning because of their simplicity and flexibility. A lot of heuristic algorithms have been proposed to construct near-optimal decision trees. ID3, C4.5 and CART are classical decision tree algorithms and the split criteria they…
This is full length article (draft version) where problem number of topics in Topic Modeling is discussed. We proposed idea that Renyi and Tsallis entropy can be used for identification of optimal number in large textual collections. We also report results of numerical experiments of Semantic stability for 4 topic mode…
Estimate relaxation times in nonextensive systems using gradient flow for Tsallis entropy maximization.
Optimal control in latent factor models uses Tsallis entropy for exploration.
This paper introduces a new potential function using Tsallis entropy for neural network optimization.
Coupled entropy corrects flaws in Tsallis entropy for complex systems.
This study uses Tsallis entropy to analyze diversification and integration in Italian stock market companies.
In this paper, we propose a novel maximum causal Tsallis entropy (MCTE) framework for imitation learning which can efficiently learn a sparse multi-modal policy distribution from demonstrations. We provide the full mathematical analysis of the proposed framework. First, the optimal solution of an MCTE problem is shown …
Study on utility maximization with Tsallis entropy in reinforcement learning.
New risk measure considers horizon risk and interest rate uncertainty.
Recently deep reinforcement learning (DRL) has achieved outstanding success on solving many difficult and large-scale RL problems. However the high sample cost required for effective learning often makes DRL unaffordable in resource-limited applications. With the aim of improving sample efficiency and learning performa…
Develops a Best-of-Both-Worlds algorithm for linear contextual bandits with Tsallis entropy.
One of the major issues studied in finance that has always intrigued, both scholars and practitioners, and to which no unified theory has yet been discovered, is the reason why prices move over time. Since there are several well-known traditional techniques in the literature to measure stock market volatility, a centra…
Paper finds a new principle for optimizing consumption and wealth using Tsallis entropy.
In this paper, we present a new class of Markov decision processes (MDPs), called Tsallis MDPs, with Tsallis entropy maximization, which generalizes existing maximum entropy reinforcement learning (RL). A Tsallis MDP provides a unified framework for the original RL problem and RL with various types of entropy, includin…
A hybrid impurity measure balances theoretical soundness and computational efficiency.
The paper calculates bounds for risk metrics and entropies under partial information constraints.
In this paper, a sparse Markov decision process (MDP) with novel causal sparse Tsallis entropy regularization is proposed.The proposed policy regularization induces a sparse and multi-modal optimal policy distribution of a sparse MDP. The full mathematical analysis of the proposed sparse MDP is provided.We first analyz…
Improves policy optimization with polylog(T) regret bounds for stochastic losses.
FINs enhance performance in diverse datasets like finance, speech, and health.
We propose a new policy iteration theory as an important extension of soft policy iteration and Soft Actor-Critic (SAC), one of the most efficient model free algorithms for deep reinforcement learning. Supported by the new theory, arbitrary entropy measures that generalize Shannon entropy, such as Tsallis entropy and R…
Unified meta-algorithm improves average performance across similar tasks in adversarial bandits.
We derive an algorithm that achieves the optimal (within constants) pseudo-regret in both adversarial and stochastic multi-armed bandits without prior knowledge of the regime and time horizon. The algorithm is based on online mirror descent (OMD) with Tsallis entropy regularization with power and reduced-varian…
Researchers explore gauge freedom in entropies of -Gaussian measures.
We study the sparse entropy-regularized reinforcement learning (ERL) problem in which the entropy term is a special form of the Tsallis entropy. The optimal policy of this formulation is sparse, i.e.,~at each state, it has non-zero probability for only a small number of actions. This addresses the main drawback of the …
Near-optimal per-action regret bounds for sleeping bandits are derived.
This paper studies Fenchel-Young losses, a generic way to construct convex loss functions from a regularization function. We analyze their properties in depth, showing that they unify many well-known loss functions and allow to create useful new ones easily. Fenchel-Young losses constructed from a generalized entropy, …
We define a novel family of algorithms for the adversarial multi-armed bandit problem, and provide a simple analysis technique based on convex smoothing. We prove two main results. First, we show that regularization via the \emph{Tsallis entropy}, which includes EXP3 as a special case, achieves the minim…
Advances FTPL results for bandit problems with unbounded perturbations.
Gradient descent converges with arbitrary stepsize for separable data under Fenchel-Young losses.
New adaptive learning rate for FTRL reduces regret to Θ(T^2/3).
This research improves value-at-risk estimation during financial crises using non-extensive statistical methods.
SMOTE is one of the oversampling techniques for balancing the datasets and it is considered as a pre-processing step in learning algorithms. In this paper, four new enhanced SMOTE are proposed that include an improved version of KNN in which the attribute weights are defined by mutual information firstly and then they …
Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynam…
The paper analyzes worst-case distortion risk metrics and weighted entropy under partial information.
The paper shows how policy regularization acts like an adversary to improve robustness.
The paper sets lower bounds for adversarial robustness in multiclass classification.
The paper analyzes ESS metrics and their connections to entropy families.
The theoretical basis for a candidate variational principle for the information bottleneck (IB) method is formulated within the ambit of the generalized nonadditive statistics of Tsallis. Given a nonadditivity parameter , the role of the \textit{additive duality} of nonadditive statistics () in relating…
In this paper we consider the space of those probability distributions which maximize the -Rényi entropy. These distributions have the same parameter space for every , and in the case these are the normal distributions. Some methods to endow this parameter space with Riemannian metric is presented: the seco…
Meta-learning improves performance across similar tasks in adversarial bandit settings.
Improved FTRL algorithm for multi-armed bandits with various regularizers and multiple optimal arms.
The Bregman divergence (Bregman distance, Bregman measure of distance) is a certain useful substitute for a distance, obtained from a well-chosen function (the "Bregman function"). Bregman functions and divergences have been extensively investigated during the last decades and have found applications in optimization, o…
Adjusted for chance measures are widely used to compare partitions/clusterings of the same data set. In particular, the Adjusted Rand Index (ARI) based on pair-counting, and the Adjusted Mutual Information (AMI) based on Shannon information theory are very popular in the clustering community. Nonetheless it is an open …
Earlier studies have shown that stock market distributions can be well described by distributions derived from Tsallis entropy, which is a generalization of Shannon entropy to non-extensive systems. In this paper, Tsallis relative entropy (TRE), which is the generalization of Kullback-Leibler relative entropy (KLRE) to…
In this communication, we describe some interrelations between generalized -entropies and a generalized version of Fisher information. In information theory, the de Bruijn identity links the Fisher information and the derivative of the entropy. We show that this identity can be extended to generalized versions of en…
We review some approaches to the understanding of fluctuations in some models used to describe socio and economic systems. Our approach builds on the development of a simple Langevin equation that characterises stochastic processes. This provides a unifying approach that allows first a straightforward description of th…