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.
Most bandit algorithm designs are purely theoretical. Therefore, they have strong regret guarantees, but also are often too conservative in practice. In this work, we pioneer the idea of algorithm design by minimizing the empirical Bayes regret, the average regret over problem instances sampled from a known distributio…
Improved neural active learning algorithms reduce regret and improve performance.
problem Improving performance and reducing regret in neural active learning for non-parametric streaming data.
method Introducing two new regret metrics and leveraging NNs for both exploitation and exploration. The algorithm uses tailored query decision-makers and full feedback.
result Achieved an instance-dependent regret upper bound improving by a multiplicative factor of O(logT) and removing the curse of dimensionality.
This paper improves binary classification methods beyond accuracy, especially in imbalanced datasets.
problem Binary classification performance metrics often fail to reflect real-world consequences, especially in imbalanced datasets.
method Derives a generalized Bayes-optimal classifier from accuracy to any performance metric, removing assumptions and providing finite-sample statistical guarantees.
result Optimal classification performance depends on class imbalance properties, providing new insights and guarantees.
Bayesian methods suffer from the problem of how to specify prior beliefs. One interesting idea is to consider worst-case priors. This requires solving a stochastic zero-sum game. In this paper, we extend well-known results from bandit theory in order to discover minimax-Bayes policies and discuss when they are practica…
The normalized maximized likelihood (NML) provides the minimax regret solution in universal data compression, gambling, and prediction, and it plays an essential role in the minimum description length (MDL) method of statistical modeling and estimation. Here we show that the normalized maximum likelihood has a Bayes-li…
Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt a variant of empirical Bayes and show that, by estimating the Gaussi…
The F-measure, which has originally been introduced in information retrieval, is nowadays routinely used as a performance metric for problems such as binary classification, multi-label classification, and structured output prediction. Optimizing this measure is a statistically and computationally challenging problem, s…
Propose an XMSE-aware mixed estimator for EB that interpolates between ML and EB shrinkage.
problem Kernel-based EB estimation may be worse than ML when the kernel is poorly aligned with the true parameter.
method An XMSE-aware mixed estimator that interpolates between ML and EB shrinkage.
result Fixed-weight XMSE is a scalar quadratic, yielding a closed-form oracle mixing weight that is no worse than both ML and the base EB estimator at the XMSE scale.
The problem of forecasting conditional probabilities of the next event given the past is considered in a general probabilistic setting. Given an arbitrary (large, uncountable) set C of predictors, we would like to construct a single predictor that performs asymptotically as well as the best predictor in C, on any data.…
Sharp inequality between TV and Hellinger distances for Gaussian mixtures.
problem Understanding the relationship between total variation and Hellinger distances for Gaussian mixtures.
method Established a general upper bound on Hellinger distance in terms of TV distance raised to a power, demonstrating sharpness with specific examples.
result The Hellinger distance between two Gaussian mixtures is bounded by the TV distance raised to a power 1−o(1), where o(1) is of order 1/loglog(1/TV).
In reinforcement learning the Q-values summarize the expected future rewards that the agent will attain. However, they cannot capture the epistemic uncertainty about those rewards. In this work we derive a new Bellman operator with associated fixed point we call the `knowledge values'. These K-values compress both the …
Adding domain knowledge to a learning system is known to improve results. In multi-parameter Bayesian frameworks, such knowledge is incorporated as a prior. On the other hand, various model parameters can have different learning rates in real-world problems, especially with skewed data. Two often-faced challenges in Op…
This paper is about index policies for minimizing (frequentist) regret in a stochastic multi-armed bandit model, inspired by a Bayesian view on the problem. Our main contribution is to prove that the Bayes-UCB algorithm, which relies on quantiles of posterior distributions, is asymptotically optimal when the reward dis…