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We develop an efficient Bayesian sequential inference framework for factor analysis models observed via various data types, such as continuous, binary and ordinal data. In the continuous data case, where it is possible to marginalise over…
Stochastic portfolio theory aims at finding relative arbitrages, i.e. trading strategies which outperform the market with probability one. Functionally generated portfolios, which are deterministic functions of the market weights, are an…
Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…
Feature selection is the problem of selecting a subset of features for a machine learning model that maximizes model quality subject to a budget constraint. For neural networks, prior methods, including those based on $\ell_1$…
We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of non-stationary correlations. For this purpose, we construct an ensemble of random correlation matrices and average…
We propose a parsimonious quantile regression framework to learn the dynamic tail behaviors of financial asset returns. Our model captures well both the time-varying characteristic and the asymmetrical heavy-tail property of financial time…
In this paper we propose an investing strategy based on neural network models combined with ideas from game-theoretic probability of Shafer and Vovk. Our proposed strategy uses parameter values of a neural network with the best performance…
We create a time series model for annual returns of three asset classes: the USA Standard & Poor (S&P) stock index, the international stock index, and the USA Bank of America investment-grade corporate bond index. Using this, we made an…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…
We introduce BayeSQP, a novel algorithm for general black-box optimization that merges the structure of sequential quadratic programming with concepts from Bayesian optimization. BayeSQP employs second-order Gaussian process surrogates for…
A sequential design problem for rank aggregation is commonly encountered in psychology, politics, marketing, sports, etc. In this problem, a decision maker is responsible for ranking $K$ items by sequentially collecting pairwise noisy…
We develop a new method for stochastic optimization using the Bayesian statistics approach. More precisely, we optimize parameters of chess engines as those data are available to us, but the method should apply to all situations where we…
The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which…
We use multi-class machine learning classifiers to identify the stocks that outperform or underperform other stocks. The resulting long-short portfolios achieve annual Sharpe ratios of 1.67 (value-weighted) and 3.35 (equal-weighted), with…
We present a new online learning algorithm for cumulative discounted gain. This learning algorithm does not use exponential weights on the experts. Instead, it uses a weighting scheme that depends on the regret of the master algorithm…
A common problem in Machine Learning and statistics consists in detecting whether the current sample in a stream of data belongs to the same distribution as previous ones, is an isolated outlier or inaugurates a new distribution of data. We…
Many contemporary machine learning models require extensive tuning of hyperparameters to perform well. A variety of methods, such as Bayesian optimization, have been developed to automate and expedite this process. However, tuning remains…
Building the future profit and loss (P&L) distribution of a portfolio holding, among other assets, highly non-linear and path-dependent derivatives is a challenging task. We provide a simple machinery where more and more assets could be…
We consider Bayesian algorithm execution (BAX), a framework for efficiently selecting evaluation points of an expensive function to infer a property of interest encoded as the output of a base algorithm. Since the base algorithm typically…