Andrei Markov didn't agree with Pavel Nekrasov, when he said independence between variables was necessary for the Weak Law of Large Numbers to be applied. When you collect independent samples, as the number of samples gets bigger, the mean of those samples converges to the true mean of the population. But Markov believed independence was not a necessary condition for the mean to converge. So he set out to define how the average of the outcomes from a process involving dependent random variables could converge over time. Thanks to this intellectual disagreement, Markov created a way to describe how random, also called stochastic, systems or processes evolve over time.

Population-level societal events, such as civil unrest and crime, often have a significant impact on our daily life. Forecasting such events is of great importance for decision-making and resource allocation. Event prediction has traditionally been challenging due to the lack of knowledge regarding the true causes and underlying mechanisms of event occurrence. In recent years, research on event forecasting has made significant progress due to two main reasons: (1) the development of machine learning and deep learning algorithms and (2) the accessibility of public data such as social media, news sources, blogs, economic indicators, and other meta-data sources. The explosive growth of data and the remarkable advancement in software/hardware technologies have led to applications of deep learning techniques in societal event studies. This paper is dedicated to providing a systematic and comprehensive overview of deep learning technologies for societal event predictions. We focus on two domains of societal events: \textit{civil unrest} and \textit{crime}. We first introduce how event forecasting problems are formulated as a machine learning prediction task. Then, we summarize data resources, traditional methods, and recent development of deep learning models for these problems. Finally, we discuss the challenges in societal event forecasting and put forward some promising directions for future research.

Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective variables, dominant transition pathways or manifolds and channels of probability flow can be of great importance for understanding and characterizing the kinetic, thermodynamic and mechanistic properties of the system. Deeptime is a general purpose Python library offering various tools to estimate dynamical models based on time-series data including conventional linear learning methods, such as Markov state models (MSMs), Hidden Markov Models and Koopman models, as well as kernel and deep learning approaches such as VAMPnets and deep MSMs. The library is largely compatible with scikit-learn, having a range of Estimator classes for these different models, but in contrast to scikit-learn also provides deep Model classes, e.g. in the case of an MSM, which provide a multitude of analysis methods to compute interesting thermodynamic, kinetic and dynamical quantities, such as free energies, relaxation times and transition paths. The library is designed for ease of use but also easily maintainable and extensible code. In this paper we introduce the main features and structure of the deeptime software.

We present a formalisation of finite Markov decision processes with rewards in the Isabelle theorem prover. We focus on the foundations required for dynamic programming and the use of reinforcement learning agents over such processes. In particular, we derive the Bellman equation from first principles (in both scalar and vector form), derive a vector calculation that produces the expected value of any policy p, and go on to prove the existence of a universally optimal policy where there is a discounting factor less than one. Lastly, we prove that the value iteration and the policy iteration algorithms work in finite time, producing an epsilon-optimal and a fully optimal policy respectively.

The idea of representing symbolic knowledge in connectionist systems has been a long-standing endeavour which has attracted much attention recently with the objective of combining machine learning and scalable sound reasoning. Early work has shown a correspondence between propositional logic and symmetrical neural networks which nevertheless did not scale well with the number of variables and whose training regime was inefficient. In this paper, we introduce Logical Boltzmann Machines (LBM), a neurosymbolic system that can represent any propositional logic formula in strict disjunctive normal form. We prove equivalence between energy minimization in LBM and logical satisfiability thus showing that LBM is capable of sound reasoning. We evaluate reasoning empirically to show that LBM is capable of finding all satisfying assignments of a class of logical formulae by searching fewer than 0.75% of the possible (approximately 1 billion) assignments. We compare learning in LBM with a symbolic inductive logic programming system, a state-of-the-art neurosymbolic system and a purely neural network-based system, achieving better learning performance in five out of seven data sets.

Attention is a state of arousal capable of dealing with limited processing bottlenecks in human beings by focusing selectively on one piece of information while ignoring other perceptible information. For decades, concepts and functions of attention have been studied in philosophy, psychology, neuroscience, and computing. Currently, this property has been widely explored in deep neural networks. Many different neural attention models are now available and have been a very active research area over the past six years. From the theoretical standpoint of attention, this survey provides a critical analysis of major neural attention models. Here we propose a taxonomy that corroborates with theoretical aspects that predate Deep Learning. Our taxonomy provides an organizational structure that asks new questions and structures the understanding of existing attentional mechanisms. In particular, 17 criteria derived from psychology and neuroscience classic studies are formulated for qualitative comparison and critical analysis on the 51 main models found on a set of more than 650 papers analyzed. Also, we highlight several theoretical issues that have not yet been explored, including discussions about biological plausibility, highlight current research trends, and provide insights for the future.

Reinforcement learning (RL) has gained increasing attraction in the academia and tech industry with launches to a variety of impactful applications and products. Although research is being actively conducted on many fronts (e.g., offline RL, performance, etc.), many RL practitioners face a challenge that has been largely ignored: determine whether a designed Markov Decision Process (MDP) is valid and meaningful. This study proposes a heuristic-based feature analysis method to validate whether an MDP is well formulated. We believe an MDP suitable for applying RL should contain a set of state features that are both sensitive to actions and predictive in rewards. We tested our method in constructed environments showing that our approach can identify certain invalid environment formulations. As far as we know, performing validity analysis for RL problem formulation is a novel direction. We envision that our tool will serve as a motivational example to help practitioners apply RL in real-world problems more easily.

This paper proposes a new sequential model learning architecture to solve partially observable Markov decision problems. Rather than compressing sequential information at every timestep as in conventional recurrent neural network-based methods, the proposed architecture generates a latent variable in each data block with a length of multiple timesteps and passes the most relevant information to the next block for policy optimization. The proposed blockwise sequential model is implemented based on self-attention, making the model capable of detailed sequential learning in partial observable settings. The proposed model builds an additional learning network to efficiently implement gradient estimation by using self-normalized importance sampling, which does not require the complex blockwise input data reconstruction in the model learning. Numerical results show that the proposed method significantly outperforms previous methods in various partially observable environments.

In many practical applications of RL, it is expensive to observe state transitions from the environment. For example, in the problem of plasma control for nuclear fusion, computing the next state for a given state-action pair requires querying an expensive transition function which can lead to many hours of computer simulation or dollars of scientific research. Such expensive data collection prohibits application of standard RL algorithms which usually require a large number of observations to learn. In this work, we address the problem of efficiently learning a policy while making a minimal number of state-action queries to the transition function. In particular, we leverage ideas from Bayesian optimal experimental design to guide the selection of state-action queries for efficient learning. We propose an acquisition function that quantifies how much information a state-action pair would provide about the optimal solution to a Markov decision process. At each iteration, our algorithm maximizes this acquisition function, to choose the most informative state-action pair to be queried, thus yielding a data-efficient RL approach. We experiment with a variety of simulated continuous control problems and show that our approach learns an optimal policy with up to $5$ -- $1,000\times$ less data than model-based RL baselines and $10^3$ -- $10^5\times$ less data than model-free RL baselines. We also provide several ablated comparisons which point to substantial improvements arising from the principled method of obtaining data.

Cooperation between agents in a multi-agent system (MAS) has become a hot topic in recent years, and many algorithms based on centralized training with decentralized execution (CTDE), such as VDN and QMIX, have been proposed. However, these methods disregard the information hidden in the individual action values. In this paper, we propose HyperGraph CoNvolution MIX (HGCN-MIX), a method that combines hypergraph convolution with value decomposition. By treating action values as signals, HGCN-MIX aims to explore the relationship between these signals via a self-learning hypergraph. Experimental results present that HGCN-MIX matches or surpasses state-of-the-art techniques in the StarCraft II multi-agent challenge (SMAC) benchmark on various situations, notably those with a number of agents.