arXiv research

Paper presents characteristic function of Tsallis q-Gaussian and its applications.

Researchers explore gauge freedom in entropies of $q$-Gaussian measures.

This work models financial market returns with asymmetric Tsallis distributions, improving fit over symmetric q-Gaussians.

Estimate relaxation times in nonextensive systems using gradient flow for Tsallis entropy maximization.

Optimal control in latent factor models uses Tsallis entropy for exploration.

In this communication, we describe some interrelations between generalized $q$-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…

This research improves value-at-risk estimation during financial crises using non-extensive statistical methods.

The behavior of stock market returns over a period of 1-60 days has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are non-Gaussian. They have fat tails indicating that the stock returns do not follow a random …

New method uses asymmetric Tsallis relative entropy for better risk assessment in financial portfolios.

New method calibrates reference distributions for bounded support.

The paper models stock returns using $q$-Gaussians and negative binomials.

New Stein identity for q-Gaussians reduces gradient variance in machine learning.

Fractional porous media equations yield q-Gaussian solutions for stock price returns.

The paper studies convergence rates of Tsallis entropic regularization in optimal transport.

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…

This paper presents an empirical investigation of the intraday Brazilian stock market price fluctuations, considering q-Gaussian distributions that emerge from a non-extensive statistical mechanics. Our results show that, when returns are measured over intervals less than one hour, the empirical distributions are well …

Simplified proof for Tsallis-INF algorithm without conjugate functions.

Modified Bakry-Émery criterion inequality for Tsallis entropy monotonicity.

We analyze the Standard & Poor's 500 stock market index from the last 22 years. The probability density function of price returns exhibits two well-distinguished regimes with self-similar structure: the first one displays strong super-diffusion together with short-time correlations, and the second one corresponds to we…

Paper finds a new principle for optimizing consumption and wealth using Tsallis entropy.

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…

A new algorithm enhances minority class representation in imbalanced datasets.

In this study, we analyze the aerospace stocks prices in order to characterize the sector behavior. The data analyzed cover the period from January 1987 to April 1999. We present a new index for the aerospace sector and we investigate the statistical characteristics of this index. Our results show that this index is we…

Develops a Best-of-Both-Worlds algorithm for linear contextual bandits with Tsallis entropy.

A hybrid impurity measure balances theoretical soundness and computational efficiency.

This work broadens calibeating to various proper losses using Bregman divergence.

This work generalizes calibeating for a broader range of proper losses using Bregman divergence.

Improved regret bounds for Tsallis-INF in adversarial bandits and corruptions.

We provide evidence that cumulative distributions of absolute normalized returns for the $100$ American companies with the highest market capitalization, uncover a critical behavior for different time scales $Δt$. Such cumulative distributions, in accordance with a variety of complex --and financial-- systems, can be m…

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.

Study analyzes stock market dynamics using Tsallis statistics and GHE, revealing pre-bubble and post-bubble market characteristics.

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 …

Recently, Mike and Farmer have constructed a very powerful and realistic behavioral model to mimick the dynamic process of stock price formation based on the empirical regularities of order placement and cancelation in a purely order-driven market, which can successfully reproduce the whole distribution of returns, not…

We find the wealth distribution for an economic agent in the financial market, in analogy with standard derivation of generaliz Boltzman (Tsallis) factor in statistical mechanics. In this respect, Tsallis entropic index separates two different regimes, the large and small size market. The Pareto like wealth distributio…

Study on utility maximization with Tsallis entropy in reinforcement learning.

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…

The paper calculates bounds for risk metrics and entropies under partial information constraints.

New risk measure considers horizon risk and interest rate uncertainty.

We developed a strategic of optimal portfolio based on information theory and Tsallis statistics. The growth rate of a stock market is defined by using $q$-deformed functions and we find that the wealth after n days with the optimal portfolio is given by a $q$-exponential function. In this context, the asymptotic optim…

A pricing principle is introduced for non-attainable claims in incomplete markets.

We recently showed that the S&P500 stock market index is well described by Tsallis non-extensive statistics and nonlinear Fokker-Planck time evolution. We argued that these results should be applicable to a broad range of markets and exchanges where anomalous diffusion and `heavy' tails of the distribution are present.…

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 $q$, the role of the \textit{additive duality} of nonadditive statistics ($q^*=2-q$) in relating…

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…

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumptio…

Sparse RSP routing improves graph exploration and classification.