Given a dataset on actions and resulting long-term rewards, a direct estimation approach fits value functions that minimize prediction error on the training data. Temporal difference learning (TD) methods instead fit value functions by minimizing the degree of temporal inconsistency between estimates made at successive time-steps. Focusing on finite state Markov chains, we provide a crisp asymptotic theory of the statistical advantages of this approach. First, we show that an intuitive inverse trajectory pooling coefficient completely characterizes the percent reduction in mean-squared error of value estimates. Depending on problem structure, the reduction could be enormous or nonexistent. Next, we prove that there can be dramatic improvements in estimates of the difference in value-to-go for two states: TD's errors are bounded in terms of a novel measure - the problem's trajectory crossing time - which can be much smaller than the problem's time horizon.

Existing models to extract temporal relations between events lack a principled method to incorporate external knowledge. In this study, we introduce Bayesian-Trans, a Bayesian learning-based method that models the temporal relation representations as latent variables and infers their values via Bayesian inference and translational functions. Compared to conventional neural approaches, instead of performing point estimation to find the best set parameters, the proposed model infers the parameters' posterior distribution directly, enhancing the model's capability to encode and express uncertainty about the predictions. Experimental results on the three widely used datasets show that Bayesian-Trans outperforms existing approaches for event temporal relation extraction. We additionally present detailed analyses on uncertainty quantification, comparison of priors, and ablation studies, illustrating the benefits of the proposed approach.

A large number of modern applications ranging from listening songs online and browsing the Web to using a navigation app on a smartphone generate a plethora of user trails. Clustering such trails into groups with a common sequence pattern can reveal significant structure in human behavior that can lead to improving user experience through better recommendations, and even prevent suicides [LMCR14]. One approach to modeling this problem mathematically is as a mixture of Markov chains. Recently, Gupta, Kumar and Vassilvitski [GKV16] introduced an algorithm (GKV-SVD) based on the singular value decomposition (SVD) that under certain conditions can perfectly recover a mixture of L chains on n states, given only the distribution of trails of length 3 (3-trail). In this work we contribute to the problem of unmixing Markov chains by highlighting and addressing two important constraints of the GKV-SVD algorithm [GKV16]: some chains in the mixture may not even be weakly connected, and secondly in practice one does not know beforehand the true number of chains. We resolve these issues in the Gupta et al. paper [GKV16]. Specifically, we propose an algebraic criterion that enables us to choose a value of L efficiently that avoids overfitting. Furthermore, we design a reconstruction algorithm that outputs the true mixture in the presence of disconnected chains and is robust to noise. We complement our theoretical results with experiments on both synthetic and real data, where we observe that our method outperforms the GKV-SVD algorithm. Finally, we empirically observe that combining an EM-algorithm with our method performs best in practice, both in terms of reconstruction error with respect to the distribution of 3-trails and the mixture of Markov Chains.

Reliable uncertainty quantification on RUL prediction is crucial for informative decision-making in predictive maintenance. In this context, we assess some of the latest developments in the field of uncertainty quantification for prognostics deep learning. This includes the state-of-the-art variational inference algorithms for Bayesian neural networks (BNN) as well as popular alternatives such as Monte Carlo Dropout (MCD), deep ensembles (DE) and heteroscedastic neural networks (HNN). All the inference techniques share the same inception deep learning architecture as a functional model. We performed hyperparameter search to optimize the main variational and learning parameters of the algorithms. The performance of the methods is evaluated on a subset of the large NASA NCMAPSS dataset for aircraft engines. The assessment includes RUL prediction accuracy, the quality of predictive uncertainty, and the possibility to break down the total predictive uncertainty into its aleatoric and epistemic parts. The results show no method clearly outperforms the others in all the situations. Although all methods are close in terms of accuracy, we find differences in the way they estimate uncertainty. Thus, DE and MCD generally provide more conservative predictive uncertainty than BNN. Surprisingly, HNN can achieve strong results without the added training complexity and extra parameters of the BNN. For tasks like active learning where a separation of epistemic and aleatoric uncertainty is required, radial BNN and MCD seem the best options.

Daily activity data that records individuals' various types of activities in daily life are widely used in many applications such as activity scheduling, activity recommendation, and policymaking. Though with high value, its accessibility is limited due to high collection costs and potential privacy issues. Therefore, simulating human activities to produce massive high-quality data is of great importance to benefit practical applications. However, existing solutions, including rule-based methods with simplified assumptions of human behavior and data-driven methods directly fitting real-world data, both cannot fully qualify for matching reality. In this paper, motivated by the classic psychological theory, Maslow's need theory describing human motivation, we propose a knowledge-driven simulation framework based on generative adversarial imitation learning. To enhance the fidelity and utility of the generated activity data, our core idea is to model the evolution of human needs as the underlying mechanism that drives activity generation in the simulation model. Specifically, this is achieved by a hierarchical model structure that disentangles different need levels, and the use of neural stochastic differential equations that successfully captures piecewise-continuous characteristics of need dynamics. Extensive experiments demonstrate that our framework outperforms the state-of-the-art baselines in terms of data fidelity and utility. Besides, we present the insightful interpretability of the need modeling. The code is available at https://github.com/tsinghua-fib-lab/SAND.

How is it that humans can solve complex planning tasks so efficiently despite limited cognitive resources? One reason is its ability to know how to use its limited computational resources to make clever choices. We postulate that people learn this ability from trial and error (metacognitive reinforcement learning). Here, we systematize models of the underlying learning mechanisms and enhance them with more sophisticated additional mechanisms. We fit the resulting 86 models to human data collected in previous experiments where different phenomena of metacognitive learning were demonstrated and performed Bayesian model selection. Our results suggest that a gradient ascent through the space of cognitive strategies can explain most of the observed qualitative phenomena, and is therefore a promising candidate for explaining the mechanism underlying metacognitive learning.

Reinforcement learning generalizes bandit problems with additional difficulties on longer planning horizon and unknown transition kernel. We show that, under some mild assumptions, *any* slowly changing adversarial bandit algorithm enjoys optimal regret in adversarial bandits can achieve optimal (in the dependency of $T$) expected regret in infinite-horizon discounted MDPs, without the presence of Bellman backups. The slowly changing property required by our generalization is mild, which is also marked by the online Markov decision process literature. We also examine the applicability of our reduction to a well-known adversarial bandit algorithm, EXP3.

Temporal domain generalization is a promising yet extremely challenging area where the goal is to learn models under temporally changing data distributions and generalize to unseen data distributions following the trends of the change. The advancement of this area is challenged by: 1) characterizing data distribution drift and its impacts on models, 2) expressiveness in tracking the model dynamics, and 3) theoretical guarantee on the performance. To address them, we propose a Temporal Domain Generalization with Drift-Aware Dynamic Neural Network (DRAIN) framework. Specifically, we formulate the problem into a Bayesian framework that jointly models the relation between data and model dynamics. We then build a recurrent graph generation scenario to characterize the dynamic graph-structured neural networks learned across different time points. It captures the temporal drift of model parameters and data distributions and can predict models in the future without the presence of future data. In addition, we explore theoretical guarantees of the model performance under the challenging temporal DG setting and provide theoretical analysis, including uncertainty and generalization error. Finally, extensive experiments on several real-world benchmarks with temporal drift demonstrate the proposed method's effectiveness and efficiency. In machine learning, researchers often assume that training and test data follow the same distribution for the trained model to work on test data with some generalizability.

The success of pre-trained contextualized representations has prompted researchers to analyze them for the presence of linguistic information. Indeed, it is natural to assume that these pre-trained representations do encode some level of linguistic knowledge as they have brought about large empirical improvements on a wide variety of NLP tasks, which suggests they are learning true linguistic generalization. In this work, we focus on intrinsic probing, an analysis technique where the goal is not only to identify whether a representation encodes a linguistic attribute but also to pinpoint where this attribute is encoded. We propose a novel latent-variable formulation for constructing intrinsic probes and derive a tractable variational approximation to the log-likelihood. Our results show that our model is versatile and yields tighter mutual information estimates than two intrinsic probes previously proposed in the literature. Finally, we find empirical evidence that pre-trained representations develop a cross-lingually entangled notion of morphosyntax.

High-quality education is one of the keys to achieving a more sustainable world. In contrast to traditional face-to-face classroom education, online education enables us to record and research a large amount of learning data for offering intelligent educational services. Knowledge Tracing (KT), which aims to monitor students' evolving knowledge state in learning, is the fundamental task to support these intelligent services. In recent years, an increasing amount of research is focused on this emerging field and considerable progress has been made. In this survey, we categorize existing KT models from a technical perspective and investigate these models in a systematic manner. Subsequently, we review abundant variants of KT models that consider more strict learning assumptions from three phases: before, during, and after learning. To better facilitate researchers and practitioners working on this field, we open source two algorithm libraries: EduData for downloading and preprocessing KT-related datasets, and EduKTM with extensible and unified implementation of existing mainstream KT models. Moreover, the development of KT cannot be separated from its applications, therefore we further present typical KT applications in different scenarios. Finally, we discuss some potential directions for future research in this fast-growing field.