Psychological curiosity plays a significant role in human intelligence to enhance learning through exploration and information acquisition. In the Artificial Intelligence (AI) community, artificial curiosity provides a natural intrinsic motivation for efficient learning as inspired by human cognitive development; meanwhile, it can bridge the existing gap between AI research and practical application scenarios, such as overfitting, poor generalization, limited training samples, high computational cost, etc. As a result, curiosity-driven learning (CDL) has become increasingly popular, where agents are self-motivated to learn novel knowledge. In this paper, we first present a comprehensive review on the psychological study of curiosity and summarize a unified framework for quantifying curiosity as well as its arousal mechanism. Based on the psychological principle, we further survey the literature of existing CDL methods in the fields of Reinforcement Learning, Recommendation, and Classification, where both advantages and disadvantages as well as future work are discussed. As a result, this work provides fruitful insights for future CDL research and yield possible directions for further improvement.

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with traditional methods. However, quantifying errors and uncertainties in NN-based inference is more complicated than in traditional methods. This is because in addition to aleatoric uncertainty associated with noisy data, there is also uncertainty due to limited data, but also due to NN hyperparameters, overparametrization, optimization and sampling errors as well as model misspecification. Although there are some recent works on uncertainty quantification (UQ) in NNs, there is no systematic investigation of suitable methods towards quantifying the total uncertainty effectively and efficiently even for function approximation, and there is even less work on solving partial differential equations and learning operator mappings between infinite-dimensional function spaces using NNs. In this work, we present a comprehensive framework that includes uncertainty modeling, new and existing solution methods, as well as evaluation metrics and post-hoc improvement approaches. To demonstrate the applicability and reliability of our framework, we present an extensive comparative study in which various methods are tested on prototype problems, including problems with mixed input-output data, and stochastic problems in high dimensions. In the Appendix, we include a comprehensive description of all the UQ methods employed, which we will make available as open-source library of all codes included in this framework.

Graphical models in probability and statistics are a core concept in the area of probabilistic reasoning and probabilistic programming-graphical models include Bayesian networks and factor graphs. In this paper we develop a new model of mixed (nondeterministic/probabilistic) automata that subsumes both nondeterministic automata and graphical probabilistic models. Mixed Automata are equipped with parallel composition, simulation relation, and support message passing algorithms inherited from graphical probabilistic models. Segala's Probabilistic Automatacan be mapped to Mixed Automata.

Unlike the classical linear model, nonlinear generative models have been addressed sparsely in the literature. This work aims to bring attention to these models and their secrecy potential. To this end, we invoke the replica method to derive the asymptotic normalized cross entropy in an inverse probability problem whose generative model is described by a Gaussian random field with a generic covariance function. Our derivations further demonstrate the asymptotic statistical decoupling of Bayesian inference algorithms and specify the decoupled setting for a given nonlinear model. The replica solution depicts that strictly nonlinear models establish an all-or-nothing phase transition: There exists a critical load at which the optimal Bayesian inference changes from being perfect to an uncorrelated learning. This finding leads to design of a new secure coding scheme which achieves the secrecy capacity of the wiretap channel. The proposed coding has a significantly smaller codebook size compared to the random coding scheme of Wyner. This interesting result implies that strictly nonlinear generative models are perfectly secured without any secure coding. We justify this latter statement through the analysis of an illustrative model for perfectly secure and reliable inference.

Bayesian nonparametric (BNP) models are a prominent tool for performing flexible inference with a natural quantification of uncertainty. Notable examples for \(T\) include normalization for random probabilities (Regazzini et al., 2003), kernel mixtures for densities (Lo, 1984) and for hazards (Dykstra and Laud, 1981; James, 2005), exponential transformations for survival functions (Doksum, 1974) and cumulative transformations for cumulative hazards (Hjort, 1990). Very often, though, the data presents some structural heterogeneity one should carefully take into account, especially when analyzing data from different sources that are related in some way. For instance this happens in the study of clinical trials of a COVID-19 vaccine in different countries or when understanding the effects of a certain policy adopted by multiple regions. In these cases, besides modeling heterogeneity, one further aims at introducing some probabilistic mechanism that allows for borrowing information across different studies.

Research on both natural intelligence (NI) and artificial intelligence (AI) generally assumes that the future resembles the past: intelligent agents or systems (what we call 'intelligence') observe and act on the world, then use this experience to act on future experiences of the same kind. We call this 'retrospective learning'. For example, an intelligence may see a set of pictures of objects, along with their names, and learn to name them. A retrospective learning intelligence would merely be able to name more pictures of the same objects. We argue that this is not what true intelligence is about. In many real world problems, both NIs and AIs will have to learn for an uncertain future. Both must update their internal models to be useful for future tasks, such as naming fundamentally new objects and using these objects effectively in a new context or to achieve previously unencountered goals. This ability to learn for the future we call 'prospective learning'. We articulate four relevant factors that jointly define prospective learning. Continual learning enables intelligences to remember those aspects of the past which it believes will be most useful in the future. Prospective constraints (including biases and priors) facilitate the intelligence finding general solutions that will be applicable to future problems. Curiosity motivates taking actions that inform future decision making, including in previously unmet situations. Causal estimation enables learning the structure of relations that guide choosing actions for specific outcomes, even when the specific action-outcome contingencies have never been observed before. We argue that a paradigm shift from retrospective to prospective learning will enable the communities that study intelligence to unite and overcome existing bottlenecks to more effectively explain, augment, and engineer intelligences.

Detecting relevant changes in dynamic time series data in a timely manner is crucially important for many data analysis tasks in real-world settings. Change point detection methods have the ability to discover changes in an unsupervised fashion, which represents a desirable property in the analysis of unbounded and unlabeled data streams. However, one limitation of most of the existing approaches is represented by their limited ability to handle multivariate and high-dimensional data, which is frequently observed in modern applications such as traffic flow prediction, human activity recognition, and smart grids monitoring. In this paper, we attempt to fill this gap by proposing WATCH, a novel Wasserstein distance-based change point detection approach that models an initial distribution and monitors its behavior while processing new data points, providing accurate and robust detection of change points in dynamic high-dimensional data. An extensive experimental evaluation involving a large number of benchmark datasets shows that WATCH is capable of accurately identifying change points and outperforming state-of-the-art methods.

Human infants acquire their verbal lexicon from minimal prior knowledge of language based on the statistical properties of phonological distributions and the co-occurrence of other sensory stimuli. In this study, we propose a novel fully unsupervised learning method discovering speech units by utilizing phonological information as a distributional cue and object information as a co-occurrence cue. The proposed method can not only (1) acquire words and phonemes from speech signals using unsupervised learning, but can also (2) utilize object information based on multiple modalities (i.e., vision, tactile, and auditory) simultaneously. The proposed method is based on the Nonparametric Bayesian Double Articulation Analyzer (NPB-DAA) discovering phonemes and words from phonological features, and Multimodal Latent Dirichlet Allocation (MLDA) categorizing multimodal information obtained from objects. In the experiment, the proposed method showed higher word discovery performance than the baseline methods. In particular, words that expressed the characteristics of the object (i.e., words corresponding to nouns and adjectives) were segmented accurately. Furthermore, we examined how learning performance is affected by differences in the importance of linguistic information. When the weight of the word modality was increased, the performance was further improved compared to the fixed condition.

We consider the problem of multiway clustering in the presence of unknown degree heterogeneity. Such data problems arise commonly in applications such as recommendation system, neuroimaging, community detection, and hypergraph partitions in social networks. The allowance of degree heterogeneity provides great flexibility in clustering models, but the extra complexity poses significant challenges in both statistics and computation. Here, we develop a degree-corrected tensor block model with estimation accuracy guarantees. We present the phase transition of clustering performance based on the notion of angle separability, and we characterize three signal-to-noise regimes corresponding to different statistical-computational behaviors. In particular, we demonstrate that an intrinsic statistical-to-computational gap emerges only for tensors of order three or greater. Further, we develop an efficient polynomial-time algorithm that provably achieves exact clustering under mild signal conditions. The efficacy of our procedure is demonstrated through two data applications, one on human brain connectome project, and another on Peru Legislation network dataset.

A fundamental challenge in Bayesian inference is efficient representation of a target distribution. Many non-parametric approaches do so by sampling a large number of points using variants of Markov Chain Monte Carlo (MCMC). We propose an MCMC variant that retains only those posterior samples which exceed a KSD threshold, which we call KSD Thinning. We establish the convergence and complexity tradeoffs for several settings of KSD Thinning as a function of the KSD threshold parameter, sample size, and other problem parameters. Finally, we provide experimental comparisons against other online nonparametric Bayesian methods that generate low-complexity posterior representations, and observe superior consistency/complexity tradeoffs. Code is available at github.com/colehawkins/KSD-Thinning.