Multi-agent reinforcement learning (MARL) can model many real world applications. However, many MARL approaches rely on epsilon greedy for exploration, which may discourage visiting advantageous states in hard scenarios. In this paper, we propose a new approach QMIX(SEG) for tackling MARL. It makes use of the value function factorization method QMIX to train per-agent policies and a novel Semantic Epsilon Greedy (SEG) exploration strategy. SEG is a simple extension to the conventional epsilon greedy exploration strategy, yet it is experimentally shown to greatly improve the performance of MARL. We first cluster actions into groups of actions with similar effects and then use the groups in a bi-level epsilon greedy exploration hierarchy for action selection. We argue that SEG facilitates semantic exploration by exploring in the space of groups of actions, which have richer semantic meanings than atomic actions. Experiments show that QMIX(SEG) largely outperforms QMIX and leads to strong performance competitive with current state-of-the-art MARL approaches on the StarCraft Multi-Agent Challenge (SMAC) benchmark.

Statistical relational AI and probabilistic logic programming have so far mostly focused on discrete probabilistic models. The reasons for this is that one needs to provide constructs to succinctly model the independencies in such models, and also provide efficient inference. Three types of independencies are important to represent and exploit for scalable inference in hybrid models: conditional independencies elegantly modeled in Bayesian networks, context-specific independencies naturally represented by logical rules, and independencies amongst attributes of related objects in relational models succinctly expressed by combining rules. This paper introduces a hybrid probabilistic logic programming language, DC#, which integrates distributional clauses' syntax and semantics principles of Bayesian logic programs. It represents the three types of independencies qualitatively. More importantly, we also introduce the scalable inference algorithm FO-CS-LW for DC#. FO-CS-LW is a first-order extension of the context-specific likelihood weighting algorithm (CS-LW), a novel sampling method that exploits conditional independencies and context-specific independencies in ground models.

Reward-free reinforcement learning (RL) considers the setting where the agent does not have access to a reward function during exploration, but must propose a near-optimal policy for an arbitrary reward function revealed only after exploring. In the the tabular setting, it is well known that this is a more difficult problem than PAC RL -- where the agent has access to the reward function during exploration -- with optimal sample complexities in the two settings differing by a factor of $|\mathcal{S}|$, the size of the state space. We show that this separation does not exist in the setting of linear MDPs. We first develop a computationally efficient algorithm for reward-free RL in a $d$-dimensional linear MDP with sample complexity scaling as $\mathcal{O}(d^2/\epsilon^2)$. We then show a matching lower bound of $\Omega(d^2/\epsilon^2)$ on PAC RL. To our knowledge, our approach is the first computationally efficient algorithm to achieve optimal $d$ dependence in linear MDPs, even in the single-reward PAC setting. Our algorithm relies on a novel procedure which efficiently traverses a linear MDP, collecting samples in any given "feature direction", and enjoys a sample complexity scaling optimally in the (linear MDP equivalent of the) maximal state visitation probability. We show that this exploration procedure can also be applied to solve the problem of obtaining "well-conditioned" covariates in linear MDPs.

We introduce a novel, probabilistic binary latent variable model to detect noisy or approximate repeats of patterns in sparse binary data. The model is based on the "Noisy-OR model" (Heckerman, 1990), used previously for disease and topic modelling. The model's capability is demonstrated by extracting structure in recordings from retinal neurons, but it can be widely applied to discover and model latent structure in noisy binary data. In the context of spiking neural data, the task is to "explain" spikes of individual neurons in terms of groups of neurons, "Cell Assemblies" (CAs), that often fire together, due to mutual interactions or other causes. The model infers sparse activity in a set of binary latent variables, each describing the activity of a cell assembly. When the latent variable of a cell assembly is active, it reduces the probabilities of neurons belonging to this assembly to be inactive. The conditional probability kernels of the latent components are learned from the data in an expectation maximization scheme, involving inference of latent states and parameter adjustments to the model. We thoroughly validate the model on synthesized spike trains constructed to statistically resemble recorded retinal responses to white noise stimulus and natural movie stimulus in data. We also apply our model to spiking responses recorded in retinal ganglion cells (RGCs) during stimulation with a movie and discuss the found structure.

We revisit the theory of importance weighted variational inference (IWVI), a promising strategy for learning latent variable models. IWVI uses new variational bounds, known as Monte Carlo objectives (MCOs), obtained by replacing intractable integrals by Monte Carlo estimates -- usually simply obtained via importance sampling. Burda, Grosse and Salakhutdinov (2016) showed that increasing the number of importance samples provably tightens the gap between the bound and the likelihood. Inspired by this simple monotonicity theorem, we present a series of nonasymptotic results that link properties of Monte Carlo estimates to tightness of MCOs. We challenge the rationale that smaller Monte Carlo variance leads to better bounds. We confirm theoretically the empirical findings of several recent papers by showing that, in a precise sense, negative correlation reduces the variational gap. We also generalise the original monotonicity theorem by considering non-uniform weights. We discuss several practical consequences of our theoretical results. Our work borrows many ideas and results from the theory of stochastic orders.

Explainable artificial intelligence (XAI) aims to make learning machines less opaque, and offers researchers and practitioners various tools to reveal the decision-making strategies of neural networks. In this work, we investigate how XAI methods can be used for exploring and visualizing the diversity of feature representations learned by Bayesian neural networks (BNNs). Our goal is to provide a global understanding of BNNs by making their decision-making strategies a) visible and tangible through feature visualizations and b) quantitatively measurable with a distance measure learned by contrastive learning. Our work provides new insights into the posterior distribution in terms of human-understandable feature information with regard to the underlying decision-making strategies. Our main findings are the following: 1) global XAI methods can be applied to explain the diversity of decision-making strategies of BNN instances, 2) Monte Carlo dropout exhibits increased diversity in feature representations compared to the multimodal posterior approximation of MultiSWAG, 3) the diversity of learned feature representations highly correlates with the uncertainty estimates, and 4) the inter-mode diversity of the multimodal posterior decreases as the network width increases, while the intra-mode diversity increases. Our findings are consistent with the recent deep neural networks theory, providing additional intuitions about what the theory implies in terms of humanly understandable concepts.

The Expectation-Maximization (EM) algorithm is a way to find maximum-likelihood estimates for model parameters when the data is incomplete, or has missing data points, or has unobserved/hidden latent variables. This is an iterative way to approximate the maximum likelihood function. While maximum likelihood estimation can find the "best fit" model for a set of data, it does not work specifically well for incomplete data sets. The more complex Expectation-Maximization (EM) algorithm can find model parameters even if you have missing data. It works by selecting random values for the missing data points and using those guesses to estimate a second set of data.

Classification algorithms try to predict the class or the label of the categorical target variable. A categorical variable typically represents qualitative data that has discrete values, such as pass/fail or low/medium/high, etc. Out of the many classification algorithms, the Naïve Bayes classifier is one of the simplest classification algorithms. The Naïve Bayes classifier is often used with large text datasets among other applications. The aim of this article is to explain how the Naive Bayes algorithm works.

In today's world, Machine learning becomes one of the popular and exciting fields of study that gives machines the ability to learn and become more accurate at predicting outcomes for the unseen data i.e, not seen the data in prior. The ideas in Machine learning overlaps and receives from Artificial Intelligence and many other related technologies. Today, machine learning is evolved from Pattern Recognition and the concept that computers can learn without being explicitly programmed to performing specific tasks. We can use the Machine Learning algorithms(e.g, Machine learning models can be classified into two types of models – Discriminative and Generative models.

This article was published as a part of the Data Science Blogathon. In this blog, we will be discussing how to perform image classification using four popular machine learning algorithms namely, Random Forest Classifier, KNN, Decision Tree Classifier, and Naive Bayes classifier. We will directly jump into implementation step-by-step. At the end of the article, you will understand why Deep Learning is preferred for image classification. However, the work demonstrated here will help serve research purposes if one desires to compare their CNN image classifier model with some machine learning algorithms.