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.
Study complexity in financial market using Shannon entropy.
The paper proves entropy power properties on Riemannian manifolds and Ricci flows.
Paper tests for time-varying entropy in stock prices, finding periods of inefficiency.
Paper compares Rényi min-entropy vs Shannon entropy for feature selection in machine learning.
Researchers calculate Shannon entropy rates of hidden Markov processes efficiently.
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…
Compressed Counting (CC) [22] was recently proposed for estimating the ath frequency moments of data streams, where 0 < a <= 2. CC can be used for estimating Shannon entropy, which can be approximated by certain functions of the ath frequency moments as a -> 1. Monitoring Shannon entropy for anomaly detection (e.g., DD…
Entropy for uniform hypergraphs defined via tensor theory.
Bayesian Monte-Carlo method assesses uncertainty in shear stress entropy models.
The paper extends entropy formulas to super Ricci flows on metric measure spaces.
New method uses SVD entropy to price artworks.
The notion of utility maximising entropy (u-entropy) of a probability density, which was introduced and studied by Slomczynski and Zastawniak (Ann. Prob 32 (2004) 2261-2285, arXiv:math.PR/0410115 v1), is extended in two directions. First, the relative u-entropy of two probability measures in arbitrary probability space…
In this note we determine the first two derivatives of the classical Boltzmann-Shannon entropy of the conjugate heat equation on general evolving manifolds. Based on the second derivative of the Boltzmann-Shannon entropy, we construct Perelman's F and W entropy in abstract geometric flows. Monotonicity of the entropies…
Accounting for the non-normality of asset returns remains challenging in robust portfolio optimization. In this article, we tackle this problem by assessing the risk of the portfolio through the "amount of randomness" conveyed by its returns. We achieve this by using an objective function that relies on the exponential…
The paper characterizes curvature-dimension conditions and related inequalities on Riemannian manifolds.
In information theory, Fisher information and Shannon information (entropy) are respectively used to quantify the uncertainty associated with the distribution modeling and the uncertainty in specifying the outcome of given variables. These two quantities are complementary and are jointly applied to information behavior…
Improves policy optimization with polylog(T) regret bounds for stochastic losses.
We develop a complexity measure for large-scale economic systems based on Shannon's concept of entropy. By adopting Leontief's perspective of the production process as a circular flow, we formulate the process as a Markov chain. Then we derive a measure of economic complexity as the average number of bits required to e…
This paper generalizes BO uncertainty measures using decision-theoretic entropies.
Proposes a new loss function for learning with noisy labels.
Cryptocurrencies have heavy-tailed return distributions, requiring diversification.
This review explores entropy applications in data analysis and machine learning.
Analyzes how BPE tokenisation affects corpus statistics and model entropy in transformer models.
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, …
A new clustering method using Bayesian techniques improves robustness and interpretability.
Paper introduces ENZ to measure significant coefficients in sparse recovery, improving over classical methods.
A novel framework infers causal direction from symbolic sequences using pattern entropy.
Paper introduces a new uncertainty measure for misclassification detection.
Estimating the entropy based on data is one of the prototypical problems in distribution property testing and estimation. For estimating the Shannon entropy of a distribution on elements with independent samples, [Paninski2004] showed that the sample complexity is sublinear in , and [Valiant--Valiant2011] showed…
Paper introduces a new measure combining entropy and Gini index.
Entropy analysis via kernel methods for probabilistic inference.
LogDet estimator improves entropy estimation in neural networks.
Kelly criterion, that maximizes the expectation value of the logarithm of wealth for bookmaker bets, gives an advantage over different class of strategies. We use projective symmetries for a explanation of this fact. Kelly's approach allows for an interesting financial interpretation of the Boltzmann/Shannon entropy. A…
The Moscow Stock Exchange was inefficient for most of 2012-2021.
In 1870s, L. Boltzmann proved the famous -theorem for the Boltzmann equation in the kinetic theory of gas and gave the statistical interpretation of the thermodynamic entropy. In 2002, G. Perelman introduced the notion of -entropy and proved the -entropy formula for the Ricci flow. This plays a crucial role in…
This paper introduces a new potential function using Tsallis entropy for neural network optimization.
We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our interest is in describing their convergence with sequence length, assuming no limit…
Proposes a scalable method for counterfactual prediction using machine learning.
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…
Estimate relaxation times in nonextensive systems using gradient flow for Tsallis entropy maximization.
We adapt tools from information theory to analyze how an observer comes to synchronize with the hidden states of a finitary, stationary stochastic process. We show that synchronization is determined by both the process's internal organization and by an observer's model of it. We analyze these components using the conve…
We prove local Poincaré inequalities under various curvature-dimension conditions which are stable under the measured Gromov-Hausdorff convergence. The first class of spaces we consider is that of weak CD(K,N) spaces as defined by Lott and Villani. The second class of spaces we study consists of spaces where we have a …
Statistical test rejects market efficiency using entropy from price returns.
This paper provides efficient algorithms for computing entropy and KL divergence in Bayesian networks.
We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol discretisations of the data. Analysing 1-minute and 5-minute price time series of 55 Exchang…
The price impact for a single trade is estimated by the immediate response on an event time scale, i.e., the immediate change of midpoint prices before and after a trade. We work out the price impacts across a correlated financial market. We quantify the asymmetries of the distributions and of the market structures of …
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…
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…