A recent research trend involves treating database index structures as Machine Learning (ML) models. In this domain, single or multiple ML models are trained to learn the mapping from keys to positions inside a data set. This class of indexes is known as "Learned Indexes." Learned indexes have demonstrated improved search performance and reduced space requirements for one-dimensional data. The concept of one-dimensional learned indexes has naturally been extended to multi-dimensional (e.g., spatial) data, leading to the development of "Learned Multi-dimensional Indexes". This survey focuses on learned multi-dimensional index structures. Specifically, it reviews the current state of this research area, explains the core concepts behind each proposed method, and classifies these methods based on several well-defined criteria. We present a taxonomy that classifies and categorizes each learned multi-dimensional index, and survey the existing literature on learned multi-dimensional indexes according to this taxonomy. Additionally, we present a timeline to illustrate the evolution of research on learned indexes. Finally, we highlight several open challenges and future research directions in this emerging and highly active field.

In this paper, we propose Posterior Sampling Reinforcement Learning for Zero-sum Stochastic Games (PSRL-ZSG), the first online learning algorithm that achieves Bayesian regret bound of $O(HS\sqrt{AT})$ in the infinite-horizon zero-sum stochastic games with average-reward criterion. Here $H$ is an upper bound on the span of the bias function, $S$ is the number of states, $A$ is the number of joint actions and $T$ is the horizon. We consider the online setting where the opponent can not be controlled and can take any arbitrary time-adaptive history-dependent strategy. Our regret bound improves on the best existing regret bound of $O(\sqrt[3]{DS^2AT^2})$ by Wei et al. (2017) under the same assumption and matches the theoretical lower bound in $T$.

Causal discovery in the presence of unobserved common causes from observational data only is a crucial but challenging problem. We categorize all possible causal relationships between two random variables into the following four categories and aim to identify one from observed data: two cases in which either of the direct causality exists, a case that variables are independent, and a case that variables are confounded by latent confounders. Although existing methods have been proposed to tackle this problem, they require unobserved variables to satisfy assumptions on the form of their equation models. In our previous study (Kobayashi et al., 2022), the first causal discovery method without such assumptions is proposed for discrete data and named CLOUD. Using Normalized Maximum Likelihood (NML) Code, CLOUD selects a model that yields the minimum codelength of the observed data from a set of model candidates. This paper extends CLOUD to apply for various data types across discrete, mixed, and continuous. We not only performed theoretical analysis to show the consistency of CLOUD in terms of the model selection, but also demonstrated that CLOUD is more effective than existing methods in inferring causal relationships by extensive experiments on both synthetic and real-world data.

Although there is mounting empirical evidence for the increase in affective polarization, few mechanistic models can explain its emergence at the population level. The question of how such a phenomenon can emerge from divergent opinions of a population on an ideological issue is still an open issue. In this paper, we establish that human normativity, that is, individual expression of normative opinions based on beliefs about the population, can lead to population-level polarization when ideological institutions distort beliefs in accordance with their objective of moving expressed opinion to one extreme. Using a game-theoretic model, we establish that individuals with more extreme opinions will have more extreme rhetoric and higher misperceptions about their outgroup members. Our model also shows that when social recommendation systems mediate institutional signals, we can observe the formation of different institutional communities, each with its unique community structure and characteristics. Using the model, we identify practical strategies platforms can implement, such as reducing exposure to signals from ideological institutions and a tailored approach to content moderation, both of which can rectify the affective polarization problem within its purview.

We study Risk-Sensitive Reinforcement Learning (RSRL) with the Optimized Certainty Equivalent (OCE) risk, which generalizes Conditional Value-at-risk (CVaR), entropic risk and Markowitz's mean-variance. Using an augmented Markov Decision Process (MDP), we propose two general meta-algorithms via reductions to standard RL: one based on optimistic algorithms and another based on policy optimization. Our optimistic meta-algorithm generalizes almost all prior RSRL theory with entropic risk or CVaR. Under discrete rewards, our optimistic theory also certifies the first RSRL regret bounds for MDPs with bounded coverability, e.g., exogenous block MDPs. Under discrete rewards, our policy optimization meta-algorithm enjoys both global convergence and local improvement guarantees in a novel metric that lower bounds the true OCE risk. Finally, we instantiate our framework with PPO, construct an MDP, and show that it learns the optimal risk-sensitive policy while prior algorithms provably fail.

Probabilistic circuits (PCs) have gained prominence in recent years as a versatile framework for discussing probabilistic models that support tractable queries and are yet expressive enough to model complex probability distributions. Nevertheless, tractability comes at a cost: PCs are less expressive than neural networks. In this paper we introduce probabilistic neural circuits (PNCs), which strike a balance between PCs and neural nets in terms of tractability and expressive power. Theoretically, we show that PNCs can be interpreted as deep mixtures of Bayesian networks. Experimentally, we demonstrate that PNCs constitute powerful function approximators.

Understanding the dimension dependency of computational complexity in high-dimensional sampling problem is a fundamental problem, both from a practical and theoretical perspective. Compared with samplers with unbiased stationary distribution, e.g., Metropolis-adjusted Langevin algorithm (MALA), biased samplers, e.g., Underdamped Langevin Dynamics (ULD), perform better in low-accuracy cases just because a lower dimension dependency in their complexities. Along this line, Freund et al. (2022) suggest that the modified Langevin algorithm with prior diffusion is able to converge dimension independently for strongly log-concave target distributions. Nonetheless, it remains open whether such property establishes for more general cases. In this paper, we investigate the prior diffusion technique for the target distributions satisfying log-Sobolev inequality (LSI), which covers a much broader class of distributions compared to the strongly log-concave ones. In particular, we prove that the modified Langevin algorithm can also obtain the dimension-independent convergence of KL divergence with different step size schedules. The core of our proof technique is a novel construction of an interpolating SDE, which significantly helps to conduct a more accurate characterization of the discrete updates of the overdamped Langevin dynamics. Our theoretical analysis demonstrates the benefits of prior diffusion for a broader class of target distributions and provides new insights into developing faster sampling algorithms.

Multiplex influence maximization (MIM) asks us to identify a set of seed users such as to maximize the expected number of influenced users in a multiplex network. MIM has been one of central research topics, especially in nowadays social networking landscape where users participate in multiple online social networks (OSNs) and their influences can propagate among several OSNs simultaneously. Although there exist a couple combinatorial algorithms to MIM, learning-based solutions have been desired due to its generalization ability to heterogeneous networks and their diversified propagation characteristics. In this paper, we introduce MIM-Reasoner, coupling reinforcement learning with probabilistic graphical model, which effectively captures the complex propagation process within and between layers of a given multiplex network, thereby tackling the most challenging problem in MIM. We establish a theoretical guarantee for MIM-Reasoner as well as conduct extensive analyses on both synthetic and real-world datasets to validate our MIM-Reasoner's performance.

Cognitive diagnosis models have been widely used in different areas, especially intelligent education, to measure users' proficiency levels on knowledge concepts, based on which users can get personalized instructions. As the measurement is not always reliable due to the weak links of the models and data, the uncertainty of measurement also offers important information for decisions. However, the research on the uncertainty estimation lags behind that on advanced model structures for cognitive diagnosis. Existing approaches have limited efficiency and leave an academic blank for sophisticated models which have interaction function parameters (e.g., deep learning-based models). To address these problems, we propose a unified uncertainty estimation approach for a wide range of cognitive diagnosis models. Specifically, based on the idea of estimating the posterior distributions of cognitive diagnosis model parameters, we first provide a unified objective function for mini-batch based optimization that can be more efficiently applied to a wide range of models and large datasets. Then, we modify the reparameterization approach in order to adapt to parameters defined on different domains. Furthermore, we decompose the uncertainty of diagnostic parameters into data aspect and model aspect, which better explains the source of uncertainty. Extensive experiments demonstrate that our method is effective and can provide useful insights into the uncertainty of cognitive diagnosis.

Asymmetric information stochastic games (\textsc{aisg}s) arise in many complex socio-technical systems, such as cyber-physical systems and IT infrastructures. Existing computational methods for \textsc{aisg}s are primarily offline and can not adapt to equilibrium deviations. Further, current methods are limited to special classes of \textsc{aisg}s to avoid belief hierarchies. To address these limitations, we propose conjectural online learning (\textsc{col}), an online method for generic \textsc{aisg}s. \textsc{col} uses a forecaster-actor-critic (\textsc{fac}) architecture where subjective forecasts are used to conjecture the opponents' strategies within a lookahead horizon, and Bayesian learning is used to calibrate the conjectures. To adapt strategies to nonstationary environments, \textsc{col} uses online rollout with cost function approximation (actor-critic). We prove that the conjectures produced by \textsc{col} are asymptotically consistent with the information feedback in the sense of a relaxed Bayesian consistency. We also prove that the empirical strategy profile induced by \textsc{col} converges to the Berk-Nash equilibrium, a solution concept characterizing rationality under subjectivity. Experimental results from an intrusion response use case demonstrate \textsc{col}'s superiority over state-of-the-art reinforcement learning methods against nonstationary attacks.