arXiv subjects

Topi Halme

Publications and source records attributed to Topi Halme.

6 recordsLinked to original sources

arXiv2026

Adaptive Sequential Change Detection using Mixtures of Predictive Distributions

This paper studies the problem of detecting a change in the distribution of a sequence of independent observations when the post-change distribution is unknown. We propose a novel change detection algorithm, termed Predictive-Mixture CuSum (PM-CuSum), which combines predictive distributions constructed from sliding windows of different lengths within a CuSum recursion. The predictive distributions are aggregated using adaptive weights based on their recent predictive performance. We show that PM-CuSum achieves first-order asymptotic optimality under mild conditions, and that its asymptotic delay bound has a smaller remainder order than what is achieved procedures using a single fixed (even oracle) window. Numerical simulations demonstrate that PM-CuSum performs well compared to existing methods. Moreover, it is demonstrated that forming likelihood ratios using full predictive distributions can substantially improve performance compared to plug-in likelihoods.

math.ST↗

arXiv2026

Multi-stream Quickest Change Detection: Foundations and Recent Advances

This paper provides an overview of recent developments in quickest change detection (QCD) for high-dimensional multi-sensor systems, with an emphasis on settings involving structural constraints and limited sensing resources. Classical QCD methodologies, while well understood in low-dimensional and fully observed regimes, face significant challenges when extended to modern applications characterized by large-scale data, constrained sampling or communication, and heterogeneous signal structures. We review key approaches for handling high dimensionality, including methods that exploit sparsity, and other forms of signal heterogeneity. Additionally, we discuss sampling constraints, where observations must be selected or acquired sequentially under resource limitations. Multi-stream applications can require making multiple detections, for example when detecting changes separately in different streams. The underlying assumptions on probability models, the types of changes taking place, commonly used decision-making criteria, performance indices, and error types are described. We also briefly discuss the application of machine learning in cases where the underlying probability models are not known or there is a need to select which sensors should monitor the phenomena because of the large scale of the system.

math.ST↗

arXiv2024

Quickest Change Detection for Multiple Data Streams Using the James-Stein Estimator

The problem of quickest change detection is studied in the context of detecting an arbitrary unknown mean-shift in multiple independent Gaussian data streams. The James-Stein estimator is used in constructing detection schemes that exhibit strong detection performance both asymptotically and non-asymptotically. Our results indicate that utilizing the James-Stein estimator in the recently developed window-limited CuSum test constitutes a uniform improvement over its typical maximum likelihood variant. That is, the proposed James-Stein version achieves a smaller detection delay simultaneously for all possible post-change parameter values and every false alarm rate constraint, as long as the number of parallel data streams is greater than three. Additionally, an alternative detection procedure that utilizes the James-Stein estimator is shown to have asymptotic detection delay properties that compare favorably to existing tests. The second-order asymptotic detection delay term is reduced in a predefined low-dimensional subspace of the parameter space, while second-order asymptotic minimaxity is preserved. The results are verified in simulations, where the proposed schemes are shown to achieve smaller detection delays compared to existing alternatives, especially when the number of data streams is large.

math.ST↗

arXiv2023

Dean Oliver's Four Factors Revisited

This paper studies the relationship between basketball teams' four factors and efficiency ratings as defined by Oliver (2004). The paper introduces an equation showing how a team's four factors in conjunction with its field goal and free throw percentages can be used to calculate its offensive rating. Moreover, the substitution of defensive four factors into the equation allows for the calculation of defensive and net ratings. To incorporate recent trends in the NBA, the paper updates the estimation for the relative frequency of possession-ending free throws which are needed to estimate the number of possessions from box score data. Sensitivity analysis of the offensive rating is performed in order to better understand the relative importance of the four factors. By examining partial derivatives of the offensive rating, the paper quantifies the marginal impact of small changes in the offensive and defensive four factors on offensive, defensive, and net ratings. Most importantly it is observed that the relationship between the four factors and efficiency ratings is non-linear and the individual factors' effect on the ratings depends on the values of the other factors. The paper also includes examples from NBA seasons spanning 1996-97 through 2022-23.

stat.AP↗

arXiv2021

Bayesian Quickest Detection of Propagating Spatial Events

Rapid detection of spatial events that propagate across a sensor network is of wide interest in many modern applications. In particular, in communications, radar, IoT, environmental monitoring, and biosurveillance, we may observe propagating fields or particles. In this paper, we propose Bayesian sequential single and multiple change-point detection procedures for the rapid detection of such phenomena. Using a dynamic programming framework we derive the structure of the optimal single-event quickest detection procedure, which minimizes the average detection delay (ADD) subject to a false alarm probability upper bound. The multi-sensor system configuration is arbitrary and sensors may be mobile. In the rare event regime, the optimal procedure converges to a more practical threshold test on the posterior probability of the change point. A convenient recursive computation of this posterior probability is derived by using the propagation characteristics of the spatial event. The ADD of the posterior probability threshold test is analyzed in the asymptotic regime, and specific analysis is conducted in the setting of detecting random Gaussian signals affected by path loss. Then, we show how the proposed procedure is easy to extend for detecting multiple propagating spatial events in parallel in a multiple hypothesis testing setting. A method that provides strict false discovery rate (FDR) control is proposed. In the simulation section, it is demonstrated that exploiting the spatial properties of the event decreases the ADD compared to procedures that do not utilize this information, even under model mismatch.

math.ST↗

arXiv2020

Bayesian Methods for Multiple Change-Point Detection with Reduced Communication

In many modern applications, large-scale sensor networks are used to perform statistical inference tasks. In this paper, we propose Bayesian methods for multiple change-point detection using a sensor network in which a fusion center (FC) can receive a data stream from each sensor. Due to communication limitations, the FC monitors only a subset of the sensors at each time slot. Since the number of change points can be high, we adopt the false discovery rate (FDR) criterion for controlling the rate of false alarms, while minimizing the average detection delay (ADD). We propose two Bayesian detection procedures that handle the communication limitations by monitoring the subset of the sensors with the highest posterior probabilities of change points having occurred. This monitoring policy aims to minimize the delay between the occurrence of each change point and its declaration using the corresponding posterior probabilities. One of the proposed procedures is more conservative than the second one in terms of having lower FDR at the expense of higher ADD. It is analytically shown that both procedures control the FDR under a specified tolerated level and are also scalable in the sense that they attain an ADD that does not increase asymptotically with the number of sensors. In addition, it is demonstrated that the proposed detection procedures are useful for trading off between reduced ADD and reduced average number of observations drawn until discovery. Numerical simulations are conducted for validating the analytical results and for demonstrating the properties of the proposed procedures.

cs.IT↗