In recent years, the Neurosymbolic framework has attracted a lot of attention in various applications, from recommender systems and information retrieval to healthcare and finance. This success is due to its stellar performance combined with attractive properties, such as learning and reasoning. The new emerging Neurosymbolic field is currently experiencing a renaissance, as novel frameworks and algorithms motivated by various practical applications are being introduced, building on top of the classical neural and reasoning problem setting. This article aims to provide a comprehensive review of significant recent developments in real-world applications of Neurosymbolic Artificial Intelligence. Specifically, we introduce a taxonomy of common Neurosymbolic applications and summarize the state-of-the-art for each of those domains. Furthermore, we identify important current trends and provide new perspectives pertaining to the future of this burgeoning field.

The Nystrom method provides an efficient sampling approach for large scale clustering problems, by generating a low-rank matrix approximation. However, existing sampling methods are limited by accuracy and computing time. This paper proposes an improved Nystrom-based clustering algorithm with a new sampling procedure, Minimum Sum of Squared Similarities (MSSS). Experiments on synthetic and real data sets show that the proposed sampling performs with higher accuracy than existing algorithms, applied to Nystrom-based spectral clustering problems. Furthermore, we provide a theoretical analysis that allows us to define the upper bound of the Frobenius norm error of the MSSS.

The Multi-armed bandit offer the advantage to learn and exploit the already learnt knowledge at the same time. This capability allows this approach to be applied in different domains, going from clinical trials where the goal is investigating the effects of different experimental treatments while minimizing patient losses, to adaptive routing where the goal is to minimize the delays in a network. This article provides a review of the recent results on applying bandit to real-life scenario and summarize the state of the art for each of these fields. Different techniques has been proposed to solve this problem setting, like epsilon-greedy, Upper confident bound (UCB) and Thompson Sampling (TS). We are showing here how this algorithms were adapted to solve the different problems of exploration exploitation.

Artificial behavioral agents are often evaluated based on their consistent behaviors and performance to take sequential actions in an environment to maximize some notion of cumulative reward. However, human decision making in real life usually involves different strategies and behavioral trajectories that lead to the same empirical outcome. Motivated by clinical literature of a wide range of neurological and psychiatric disorders, we propose here a more general and flexible parametric framework for sequential decision making that involves a two-stream reward processing mechanism. We demonstrated that this framework is flexible and unified enough to incorporate a family of problems spanning multi-armed bandits (MAB), contextual bandits (CB) and reinforcement learning (RL), which decompose the sequential decision making process in different levels. Inspired by the known reward processing abnormalities of many mental disorders, our clinically-inspired agents demonstrated interesting behavioral trajectories and comparable performance on simulated tasks with particular reward distributions, a real-world dataset capturing human decision-making in gambling tasks, and the PacMan game across different reward stationarities in a lifelong learning setting.

Prisoner's Dilemma mainly treat the choice to cooperate or defect as an atomic action. We propose to study online learning algorithm behavior in the Iterated Prisoner's Dilemma (IPD) game, where we explored the full spectrum of reinforcement learning agents: multi-armed bandits, contextual bandits and reinforcement learning. We have evaluate them based on a tournament of iterated prisoner's dilemma where multiple agents can compete in a sequential fashion. This allows us to analyze the dynamics of policies learned by multiple self-interested independent reward-driven agents, and also allows us study the capacity of these algorithms to fit the human behaviors. Results suggest that considering the current situation to make decision is the worst in this kind of social dilemma game. Multiples discoveries on online learning behaviors and clinical validations are stated.

Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating algorithms are proposed, including the Nystrom method - an approach with proven approximate error bounds. There are several algorithms that provide recipes to construct Nystrom approximations with variable accuracies and computing times. This paper proposes a scalable Nystrom-based clustering algorithm with a new sampling procedure, Centroid Minimum Sum of Squared Similarities (CMS3), and a heuristic on when to use it. Our heuristic depends on the eigen spectrum shape of the dataset, and yields competitive low-rank approximations in test datasets compared to the other state-of-the-art methods

Dirichlet-multinomial (DMN) distribution is commonly used to model over-dispersion in count data. Precise and fast numerical computation of the DMN log-likelihood function is important for performing statistical inference using this distribution, and remains a challenge. To address this, we use mathematical properties of the gamma function to derive a closed form expression for the DMN log-likelihood function. Compared to existing methods, calculation of the closed form has a lower computational complexity, hence is much faster without comprimising computational accuracy.

The CASH problem has been widely studied in the context of automated configurations of machine learning (ML) pipelines and various solvers and toolkits are available. However, CASH solvers do not directly handle black-box constraints such as fairness, robustness or other domain-specific custom constraints. We present our recent approach [Liu, et al., 2020] that leverages the ADMM optimization framework to decompose CASH into multiple small problems and demonstrate how ADMM facilitates incorporation of black-box constraints.

We study here the problem of learning the exploration exploitation trade-off in the contextual bandit problem with linear reward function setting. In the traditional algorithms that solve the contextual bandit problem, the exploration is a parameter that is tuned by the user. However, our proposed algorithm learn to choose the right exploration parameters in an online manner based on the observed context, and the immediate reward received for the chosen action. We have presented here two algorithms that uses a bandit to find the optimal exploration of the contextual bandit algorithm, which we hope is the first step toward the automation of the multi-armed bandit algorithm.

We consider the stochastic multi-armed bandit problem and the contextual bandit problem with historical observations and pre-clustered arms. The historical observations can contain any number of instances for each arm, and the pre-clustering information is a fixed clustering of arms provided as part of the input. We develop a variety of algorithms which incorporate this offline information effectively during the online exploration phase and derive their regret bounds. In particular, we develop the META algorithm which effectively hedges between two other algorithms: one which uses both historical observations and clustering, and another which uses only the historical observations. The former outperforms the latter when the clustering quality is good, and vice-versa. Extensive experiments on synthetic and real world datasets on Warafin drug dosage and web server selection for latency minimization validate our theoretical insights and demonstrate that META is a robust strategy for optimally exploiting the pre-clustering information.