Reinforcement Learning (RL) applied to financial problems has been the subject of a lively area of research. The use of RL for optimal trading strategies that exploit latent information in the market is, to the best of our knowledge, not widely tackled. In this paper we study an optimal trading problem, where a trading signal follows an Ornstein-Uhlenbeck process with regime-switching dynamics. We employ a blend of RL and Recurrent Neural Networks (RNN) in order to make the most at extracting underlying information from the trading signal with latent parameters. The latent parameters driving mean reversion, speed, and volatility are filtered from observations of the signal, and trading strategies are derived via RL. To address this problem, we propose three Deep Deterministic Policy Gradient (DDPG)-based algorithms that integrate Gated Recurrent Unit (GRU) networks to capture temporal dependencies in the signal. The first, a one -step approach (hid-DDPG), directly encodes hidden states from the GRU into the RL trader. The second and third are two-step methods: one (prob-DDPG) makes use of posterior regime probability estimates, while the other (reg-DDPG) relies on forecasts of the next signal value. Through extensive simulations with increasingly complex Markovian regime dynamics for the trading signal's parameters, as well as an empirical application to equity pair trading, we find that prob-DDPG achieves superior cumulative rewards and exhibits more interpretable strategies. By contrast, reg-DDPG provides limited benefits, while hid-DDPG offers intermediate performance with less interpretable strategies. Our results show that the quality and structure of the information supplied to the agent are crucial: embedding probabilistic insights into latent regimes substantially improves both profitability and robustness of reinforcement learning-based trading strategies.

This article establishes a rigorous spectral framework for the mathematical analysis of SHAP values. We show that any predictive model defined on a discrete or multi-valued input space admits a generalized Fourier expansion with respect to an orthonormalisation tensor-product basis constructed under a product probability measure. Within this setting, each SHAP attribution can be represented as a linear functional of the model's Fourier coefficients. Two complementary regimes are studied. In the deterministic regime, we derive quantitative stability estimates for SHAP values under Fourier truncation, showing that the attribution map is Lipschitz continuous with respect to the distance between predictors. In the probabilistic regime, we consider neural networks in their infinite-width limit and prove convergence of SHAP values toward those induced by the corresponding Gaussian process prior, with explicit error bounds in expectation and with high probability based on concentration inequalities. We also provide a numerical experiment on a clinical unbalanced dataset to validate the theoretical findings.

We present MMbeddings, a probabilistic embedding approach that reinterprets categorical embeddings through the lens of nonlinear mixed models, effectively bridging classical statistical theory with modern deep learning. By treating embeddings as latent random effects within a variational autoencoder framework, our method substantially decreases the number of parameters -- from the conventional embedding approach of cardinality $\times$ embedding dimension, which quickly becomes infeasible with large cardinalities, to a significantly smaller, cardinality-independent number determined primarily by the encoder architecture. This reduction dramatically mitigates overfitting and computational burden in high-cardinality settings. Extensive experiments on simulated and real datasets, encompassing collaborative filtering and tabular regression tasks using varied architectures, demonstrate that MMbeddings consistently outperforms traditional embeddings, underscoring its potential across diverse machine learning applications.

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China's president Xi caught knifing Trump in brutal attack just hours after historic summit World's'most trusted' broadcaster the BBC doctored Trump speech a week before the election, whistleblower reveals I won't ever forget what I saw at Andy Cohen's party. He may admit he's hooking up with guys on every dating app but this is the truth about men like him: KENNEDY'Venomous' Republican split over Israel hits new low as fiery feud reaches White House America's most dangerous cities revealed: Crime, natural disaster risks and financial safety top the list of growing concerns Drivers mock new design for world's best-selling car: 'Did it already get into a wreck?' I learned the horrifying risks of'miracle' ADHD drugs and stopped taking them... but it was too late Roller coaster camera caught utter terror on people's faces after seat belt failed on 208ft ride that travels at 75mph The leafy suburb under an hour from Manhattan where wealthy New Yorkers are fleeing to escape'woke' Mamdani's socialist dystopia The five cities with America's most pleasant climate revealed - and they're all in the same state A girl, 15, bludgeoned to death in a gated enclave, a Kennedy cousin released and the brother who'knows the truth' about the death that haunts Camelot Sex aids and poppers... the sordid discoveries made by royal aides after party Andrew threw for Epstein and Ghislaine Maxwell - and the truth about those massages: ROBERT JOBSON READ MORE: New Jersey UFO mystery solved! Mysterious drones were spotted near Belgium's Kleine Brogel air base, where US nuclear weapons are stored, prompting fears of a potential espionage operation. Belgium's Defense Minister Theo Francken confirmed that drones entered the base's airspace in two waves on Saturday and Sunday night.

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This material may not be published, broadcast, rewritten, or redistributed. Quotes displayed in real-time or delayed by at least 15 minutes. Market data provided by Factset . Powered and implemented by FactSet Digital Solutions . Mutual Fund and ETF data provided by Refinitiv Lipper .

This month's full moon will come within about 222,000 miles of Earth. The supermoon rises from the sea in Molfetta, Italy, on October 7, 2025. It was the first of three consecutive supermoons in 2025. Breakthroughs, discoveries, and DIY tips sent every weekday. As the year's penultimate month kicks off, the year's brightest supermoon is almost here.

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