The spread in the use of tracking systems in sport has made fine-grained spatiotemporal analysis a primary focus of an emerging sports analytics industry. Recently publicized tracking data for men's professional tennis allows for the first detailed spatial analysis of return impact. Mixture models are an appealing model-based framework for spatial analysis in sport, where latent variable discovery is often of primary interest. Although finite mixture models have the advantages of interpretability and scalability, most implementations assume standard parametric distributions for outcomes conditioned on latent variables. In this paper, we present a more flexible alternative that allows the latent conditional distribution to be a mixed member of finite Gaussian mixtures. Our model was motivated by our efforts to describe common styles of return impact location of professional tennis players and is the reason we name the approach a 'latent style allocation' model. In a fully Bayesian implementation, we apply the model to 142,803 return points played by 141 top players at Association of Tennis Professional events between 2018 and 2020 and show that the latent style allocation improves predictive performance over a finite Gaussian mixture model and identifies six unique impact styles on the first and second serve return.
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Representation is a key notion in neuroscience and artificial intelligence (AI). However, a longstanding philosophical debate highlights that specifying what counts as representation is trickier than it seems. With this brief opinion paper we would like to bring the philosophical problem of representation into attention and provide an implementable solution. We note that causal and teleological approaches often assumed by neuroscientists and engineers fail to provide a satisfactory account of representation. We sketch an alternative according to which representations correspond to inferred latent structures in the world, identified on the basis of conditional patterns of activation. These structures are assumed to have certain properties objectively, which allows for planning, prediction, and detection of unexpected events. We illustrate our proposal with the simulation of a simple neural network model. We believe this stronger notion of representation could inform future research in neuroscience and AI.
Probabilistic databases (PDBs) are probability spaces over database instances. They provide a framework for handling uncertainty in databases, as occurs due to data integration, noisy data, data from unreliable sources or randomized processes. Most of the existing theory literature investigated finite, tuple-independent PDBs (TI-PDBs) where the occurrences of tuples are independent events. Only recently, Grohe and Lindner (PODS '19) introduced independence assumptions for PDBs beyond the finite domain assumption. In the finite, a major argument for discussing the theoretical properties of TI-PDBs is that they can be used to represent any finite PDB via views. This is no longer the case once the number of tuples is countably infinite. In this paper, we systematically study the representability of infinite PDBs in terms of TI-PDBs and the related block-independent disjoint PDBs. The central question is which infinite PDBs are representable as first-order views over tuple-independent PDBs. We give a necessary condition for the representability of PDBs and provide a sufficient criterion for representability in terms of the probability distribution of a PDB. With various examples, we explore the limits of our criteria. We show that conditioning on first order properties yields no additional power in terms of expressivity. Finally, we discuss the relation between purely logical and arithmetic reasons for (non-)representability.
Developing technology and changing lifestyles have made online grocery delivery applications an indispensable part of urban life. Since the beginning of the COVID-19 pandemic, the demand for such applications has dramatically increased, creating new competitors that disrupt the market. An increasing level of competition might prompt companies to frequently restructure their marketing and product pricing strategies. Therefore, identifying the change patterns in product prices and sales volumes would provide a competitive advantage for the companies in the marketplace. In this paper, we investigate alternative clustering methodologies to group the products based on the price patterns and sales volumes. We propose a novel distance metric that takes into account how product prices and sales move together rather than calculating the distance using numerical values. We compare our approach with traditional clustering algorithms, which typically rely on generic distance metrics such as Euclidean distance, and image clustering approaches that aim to group data by capturing its visual patterns. We evaluate the performances of different clustering algorithms using our custom evaluation metric as well as Calinski Harabasz and Davies Bouldin indices, which are commonly used internal validity metrics. We conduct our numerical study using a propriety price dataset from an online food and grocery delivery company, and the publicly available Favorita sales dataset. We find that our proposed clustering approach and image clustering both perform well for finding the products with similar price and sales patterns within large datasets.
In this study, we examine a clustering problem in which the covariates of each individual element in a dataset are associated with an uncertainty specific to that element. More specifically, we consider a clustering approach in which a pre-processing applying a non-linear transformation to the covariates is used to capture the hidden data structure. To this end, we approximate the sets representing the propagated uncertainty for the pre-processed features empirically. To exploit the empirical uncertainty sets, we propose a greedy and optimistic clustering (GOC) algorithm that finds better feature candidates over such sets, yielding more condensed clusters. As an important application, we apply the GOC algorithm to synthetic datasets of the orbital properties of stars generated through our numerical simulation mimicking the formation process of the Milky Way. The GOC algorithm demonstrates an improved performance in finding sibling stars originating from the same dwarf galaxy. These realistic datasets have also been made publicly available.
We develop an unsupervised probabilistic model for heterogeneous Electronic Health Record (EHR) data. Utilizing a mixture model formulation, our approach directly models sequences of arbitrary length, such as medications and laboratory results. This allows for subgrouping and incorporation of the dynamics underlying heterogeneous data types. The model consists of a layered set of latent variables that encode underlying structure in the data. These variables represent subject subgroups at the top layer, and unobserved states for sequences in the second layer. We train this model on episodic data from subjects receiving medical care in the Kaiser Permanente Northern California integrated healthcare delivery system. The resulting properties of the trained model generate novel insight from these complex and multifaceted data. In addition, we show how the model can be used to analyze sequences that contribute to assessment of mortality likelihood.
Factor analysis is often used to assess whether a single univariate latent variable is sufficient to explain most of the covariance among a set of indicators for some underlying construct. When evidence suggests that a single factor is adequate, research often proceeds by using a univariate summary of the indicators in subsequent research. Implicit in such practices is the assumption that it is the underlying latent, rather than the indicators, that is causally efficacious. The assumption that the indicators do not have effects on anything subsequent, and that they are themselves only affected by antecedents through the underlying latent is a strong assumption, effectively imposing a structural interpretation on the latent factor model. In this paper, we show that this structural assumption has empirically testable implications, even though the latent variable itself is unobserved. We develop a statistical test to potentially reject the structural interpretation of a latent factor model. We apply this test to data concerning associations between the Satisfaction-with-Life-Scale and subsequent all-cause mortality, which provides strong evidence against a structural interpretation for a univariate latent underlying the scale. Discussion is given to the implications of this result for the development, evaluation, and use of measures and for the use of factor analysis itself.
Reinforcement learning (RL) has shown great success in solving many challenging tasks via use of deep neural networks. Although using deep learning for RL brings immense representational power, it also causes a well-known sample-inefficiency problem. This means that the algorithms are data-hungry and require millions of training samples to converge to an adequate policy. One way to combat this issue is to use action advising in a teacher-student framework, where a knowledgeable teacher provides action advice to help the student. This work considers how to better leverage uncertainties about when a student should ask for advice and if the student can model the teacher to ask for less advice. The student could decide to ask for advice when it is uncertain or when both it and its model of the teacher are uncertain. In addition to this investigation, this paper introduces a new method to compute uncertainty for a deep RL agent using a secondary neural network. Our empirical results show that using dual uncertainties to drive advice collection and reuse may improve learning performance across several Atari games.
We present a novel static analysis technique to derive higher moments for program variables for a large class of probabilistic loops with potentially uncountable state spaces. Our approach is fully automatic, meaning it does not rely on externally provided invariants or templates. We employ algebraic techniques based on linear recurrences and introduce program transformations to simplify probabilistic programs while preserving their statistical properties. We develop power reduction techniques to further simplify the polynomial arithmetic of probabilistic programs and define the theory of moment-computable probabilistic loops for which higher moments can precisely be computed. Our work has applications towards recovering probability distributions of random variables and computing tail probabilities. The empirical evaluation of our results demonstrates the applicability of our work on many challenging examples.
We recall some of the history of the information-theoretic approach to deriving core results in probability theory and indicate parts of the recent resurgence of interest in this area with current progress along several interesting directions. Then we give a new information-theoretic proof of a finite version of de Finetti's classical representation theorem for finite-valued random variables. We derive an upper bound on the relative entropy between the distribution of the first $k$ in a sequence of $n$ exchangeable random variables, and an appropriate mixture over product distributions. The mixing measure is characterised as the law of the empirical measure of the original sequence, and de Finetti's result is recovered as a corollary. The proof is nicely motivated by the Gibbs conditioning principle in connection with statistical mechanics, and it follows along an appealing sequence of steps. The technical estimates required for these steps are obtained via the use of a collection of combinatorial tools known within information theory as `the method of types.'
Alerts are crucial for requesting prompt human intervention upon cloud anomalies. The quality of alerts significantly affects the cloud reliability and the cloud provider's business revenue. In practice, we observe on-call engineers being hindered from quickly locating and fixing faulty cloud services because of the vast existence of misleading, non-informative, non-actionable alerts. We call the ineffectiveness of alerts "anti-patterns of alerts". To better understand the anti-patterns of alerts and provide actionable measures to mitigate anti-patterns, in this paper, we conduct the first empirical study on the practices of mitigating anti-patterns of alerts in an industrial cloud system. We study the alert strategies and the alert processing procedure at Huawei Cloud, a leading cloud provider. Our study combines the quantitative analysis of millions of alerts in two years and a survey with eighteen experienced engineers. As a result, we summarized four individual anti-patterns and two collective anti-patterns of alerts. We also summarize four current reactions to mitigate the anti-patterns of alerts, and the general preventative guidelines for the configuration of alert strategy. Lastly, we propose to explore the automatic evaluation of the Quality of Alerts (QoA), including the indicativeness, precision, and handleability of alerts, as a future research direction that assists in the automatic detection of alerts' anti-patterns. The findings of our study are valuable for optimizing cloud monitoring systems and improving the reliability of cloud services.
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