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This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…

Optimization and Control · Mathematics 2023-01-13 Emiland Garrabe , Giovanni Russo

The forecasting combination puzzle is a well-known phenomenon in forecasting literature, stressing the challenge of outperforming the simple average when aggregating forecasts from diverse methods. This study proposes a Reinforcement…

Econometrics · Economics 2025-08-29 Marcelo C. Medeiros , Jeronymo M. Pinro

Confidence sequences are collections of confidence regions that simultaneously cover the true parameter for every sample size at a prescribed confidence level. Tightening these sequences is of practical interest and can be achieved by…

Methodology · Statistics 2026-05-11 Stefano Cortinovis , Valentin Kilian , François Caron

The goal of this paper is to demonstrate the general modeling and practical simulation of random equations with mixture model parameter random variables. Random equations, understood as stationary (non-dynamical) equations with parameters…

Computation · Statistics 2025-07-31 Wolfgang Hoegele

In recent decades, new methods and approaches have been developed for forecasting intermittent demand series. However, the majority of research has focused on point forecasting, with little exploration into probabilistic intermittent demand…

Applications · Statistics 2024-04-16 Shengjie Wang , Yanfei Kang , Fotios Petropoulos

In finite probability theory, events are subsets of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce "superposition events."…

Quantum Physics · Physics 2020-06-18 David Ellerman

Large collections of time series data are often organized into hierarchies with different levels of aggregation; examples include product and geographical groupings. Probabilistic coherent forecasting is tasked to produce forecasts…

Continual learning in environments with shifting data distributions is a challenging problem with several real-world applications. In this paper we consider settings in which the data distribution(task) shifts abruptly and the timing of…

Machine Learning · Computer Science 2022-01-07 Mengda Xu , Sumitra Ganesh , Pranay Pasula

Forecast combination integrates information from various sources by consolidating multiple forecast results from the target time series. Instead of the need to select a single optimal forecasting model, this paper introduces a deep learning…

Machine Learning · Computer Science 2023-11-27 Yinuo Ren , Feng Li , Yanfei Kang , Jue Wang

Forecast combinations have flourished remarkably in the forecasting community and, in recent years, have become part of the mainstream of forecasting research and activities. Combining multiple forecasts produced from single (target) series…

Methodology · Statistics 2022-09-26 Xiaoqian Wang , Rob J Hyndman , Feng Li , Yanfei Kang

The problem is sequence prediction in the following setting. A sequence $x_1,...,x_n,...$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, it is required…

Artificial Intelligence · Computer Science 2012-03-20 Daniil Ryabko

Asynchronous event sequence clustering aims to group similar event sequences in an unsupervised manner. Mixture models of temporal point processes have been proposed to solve this problem, but they often suffer from overfitting, leading to…

Machine Learning · Computer Science 2024-11-08 Yiwei Dong , Shaoxin Ye , Yuwen Cao , Qiyu Han , Hongteng Xu , Hanfang Yang

A multicomponent random process used as a model for the problem of space-time earthquake prediction; this allows us to develop consistent estimation for conditional probabilities of large earthquakes if the values of the predictor…

Geophysics · Physics 2009-04-28 V. M. Ghertzik

We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…

Machine Learning · Computer Science 2014-01-24 N. Denizcan Vanli , Suleyman S. Kozat

In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…

Information Theory · Computer Science 2025-01-07 Ching-Fang Li , I-Hsiang Wang

We study the problem of sequentially predicting properties of a probabilistic model and its next outcome over an infinite horizon, with the goal of ensuring that the predictions incur only finitely many errors with probability 1. We…

Statistics Theory · Mathematics 2024-02-08 Changlong Wu , Narayana Santhanam

The problem of sequential probability forecasting is considered in the most general setting: a model set C is given, and it is required to predict as well as possible if any of the measures (environments) in C is chosen to generate the…

Machine Learning · Computer Science 2019-10-25 Daniil Ryabko

Since its introduction, the transformer has shifted the development trajectory away from traditional models (e.g., RNN, MLP) in time series forecasting, which is attributed to its ability to capture global dependencies within temporal…

Machine Learning · Computer Science 2025-01-07 Xiwen Chen , Peijie Qiu , Wenhui Zhu , Huayu Li , Hao Wang , Aristeidis Sotiras , Yalin Wang , Abolfazl Razi

Predicting the future is an important component of decision making. In most situations, however, there is not enough information to make accurate predictions. In this paper, we develop a theory of causal reasoning for predictive inference…

Artificial Intelligence · Computer Science 2013-04-10 Thomas L. Dean , Keiji Kanazawa

The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…

Machine Learning · Computer Science 2010-06-29 Shankar Vembu