Machine Learning is a division of AI that focuses on building applications by processing available data accurately. The primary aim of machine learning is to help computers process calculations without human intervention. The question that arises here is, so how do we feed the data to the machine? How would the machine now perform operations on this dataset and provide precise results? This is where mathematics comes into play.

Naive Bayes Classifier is a simple model that's usually used in classification problems. Despite being simple, it has shown very good results, outperforming by far other, more complicated models. This is the second article in a series of two about the Naive Bayes Classifier and it will deal with the implementation of the model in Scikit-Learn with Python. For a detailed overview of the math and the principles behind the model, please check the other article: Naive Bayes Classifier Explained. In the previous article linked above, I introduced a table of some data that we can train our classifier on.

Success is a process not an event. Data Science is growing rapidly in all sectors. With the availability of so many technologies within the Data Science domain, it becomes tricky to crack any Data Science interview. In this article, we have tried to cover the most common Data Science interview questions asked by recruiters. Answer: The question can also be phrased as to why linear regression is not a very effective algorithm.

Sparse Bayesian Learning (SBL) constructs an extremely sparse probabilistic model with very competitive generalization. However, SBL needs to invert a big covariance matrix with complexity O(M^3 ) (M: feature size) for updating the regularization priors, making it difficult for practical use. There are three issues in SBL: 1) Inverting the covariance matrix may obtain singular solutions in some cases, which hinders SBL from convergence; 2) Poor scalability to problems with high dimensional feature space or large data size; 3) SBL easily suffers from memory overflow for large-scale data. This paper addresses these issues with a newly proposed diagonal Quasi-Newton (DQN) method for SBL called DQN-SBL where the inversion of big covariance matrix is ignored so that the complexity and memory storage are reduced to O(M). The DQN-SBL is thoroughly evaluated on non-linear classifiers and linear feature selection using various benchmark datasets of different sizes. Experimental results verify that DQN-SBL receives competitive generalization with a very sparse model and scales well to large-scale problems.

So far, most research on recommender systems focused on maintaining long-term user engagement and satisfaction, by promoting relevant and personalized content. However, it is still very challenging to evaluate the quality and the reliability of this content. In this paper, we propose FEBR (Expert-Based Recommendation Framework), an apprenticeship learning framework to assess the quality of the recommended content on online platforms. The framework exploits the demonstrated trajectories of an expert (assumed to be reliable) in a recommendation evaluation environment, to recover an unknown utility function. This function is used to learn an optimal policy describing the expert's behavior, which is then used in the framework to provide high-quality and personalized recommendations. We evaluate the performance of our solution through a user interest simulation environment (using RecSim). We simulate interactions under the aforementioned expert policy for videos recommendation, and compare its efficiency with standard recommendation methods. The results show that our approach provides a significant gain in terms of content quality, evaluated by experts and watched by users, while maintaining almost the same watch time as the baseline approaches.

Policy optimization methods are among the most widely-used methods in reinforcement learning. Its empirical success has been demonstrated in various domains such as computer games [Schulman et al., 2017] and robotics [Levine and Koltun, 2013]. However, due to its local-search nature, global optimality guarantees of policy optimization often rely on unrealistic assumptions to ensure global exploration (see e.g., [Abbasi-Yadkori et al., 2019, Agarwal et al., 2020b, Neu and Olkhovskaya, 2020, Wei et al., 2021]), making it theoretically less appealing compared to other methods. Motivated by this issue, a line of recent works [Cai et al., 2020, Shani et al., 2020, Agarwal et al., 2020a, Zanette et al., 2021] equip policy optimization with global exploration by adding exploration bonuses to the update, and prove favorable guarantees even without making extra exploratory assumptions. Moreover, they all demonstrate some robustness aspect of policy optimization (such as being able to handle adversarial losses or a certain degree of model misspecification). Despite these important progresses, however, many limitations still exist, including worse regret rates comparing to the best value-based or model-based approaches [Shani et al., 2020, Agarwal et al., 2020a, Zanette et al., 2021], or requiring full-information feedback on the entire loss function (as opposed to the more realistic bandit feedback) [Cai et al., 2020]. To address these issues, in this work, we propose a new type of exploration bonuses called dilated bonuses, which satisfies a certain dilated Bellman equation and provably leads to improved exploration compared to existing works (Section 3). We apply this general idea to advance the state-of-the-art of policy optimization for learning finite-horizon episodic MDPs with adversarial losses and bandit feedback. More specifically, our main results are: - First, in the tabular setting, addressing the main open question left in [Shani et al., 2020], we improve their Õ(T

Probabilistic graphical models are a fundamental tool in probabilistic modeling, machine learning and artificial intelligence. They allow us to integrate in a natural way expert knowledge, physical modeling, heterogeneous and correlated data and quantities of interest. For exactly this reason, multiple sources of model uncertainty are inherent within the modular structure of the graphical model. In this paper we develop information-theoretic, robust uncertainty quantification methods and non-parametric stress tests for directed graphical models to assess the effect and the propagation through the graph of multi-sourced model uncertainties to quantities of interest. These methods allow us to rank the different sources of uncertainty and correct the graphical model by targeting its most impactful components with respect to the quantities of interest. Thus, from a machine learning perspective, we provide a mathematically rigorous approach to correctability that guarantees a systematic selection for improvement of components of a graphical model while controlling potential new errors created in the process in other parts of the model. We demonstrate our methods in two physico-chemical examples, namely quantum scale-informed chemical kinetics and materials screening to improve the efficiency of fuel cells.

Autonomous car racing is a challenging task in the robotic control area. Traditional modular methods require accurate mapping, localization and planning, which makes them computationally inefficient and sensitive to environmental changes. Recently, deep-learning-based end-to-end systems have shown promising results for autonomous driving/racing. However, they are commonly implemented by supervised imitation learning (IL), which suffers from the distribution mismatch problem, or by reinforcement learning (RL), which requires a huge amount of risky interaction data. In this work, we present a general deep imitative reinforcement learning approach (DIRL), which successfully achieves agile autonomous racing using visual inputs. The driving knowledge is acquired from both IL and model-based RL, where the agent can learn from human teachers as well as perform self-improvement by safely interacting with an offline world model. We validate our algorithm both in a high-fidelity driving simulation and on a real-world 1/20-scale RC-car with limited onboard computation. The evaluation results demonstrate that our method outperforms previous IL and RL methods in terms of sample efficiency and task performance. Demonstration videos are available at https://caipeide.github.io/autorace-dirl/

In many common-payoff games, achieving good performance requires players to develop protocols for communicating their private information implicitly -- i.e., using actions that have non-communicative effects on the environment. Multi-agent reinforcement learning practitioners typically approach this problem using independent learning methods in the hope that agents will learn implicit communication as a byproduct of expected return maximization. Unfortunately, independent learning methods are incapable of doing this in many settings. In this work, we isolate the implicit communication problem by identifying a class of partially observable common-payoff games, which we call implicit referential games, whose difficulty can be attributed to implicit communication. Next, we introduce a principled method based on minimum entropy coupling that leverages the structure of implicit referential games, yielding a new perspective on implicit communication. Lastly, we show that this method can discover performant implicit communication protocols in settings with very large spaces of messages.

Labeled data is essential in modern systems that rely on Machine Learning (ML) for predictive modelling. Such systems may suffer from the cold-start problem: supervised models work well but, initially, there are no labels, which are costly or slow to obtain. This problem is even worse in imbalanced data scenarios. Online financial fraud detection is an example where labeling is: i) expensive, or ii) it suffers from long delays, if relying on victims filing complaints. The latter may not be viable if a model has to be in place immediately, so an option is to ask analysts to label events while minimizing the number of annotations to control costs. We propose an Active Learning (AL) annotation system for datasets with orders of magnitude of class imbalance, in a cold start streaming scenario. We present a computationally efficient Outlier-based Discriminative AL approach (ODAL) and design a novel 3-stage sequence of AL labeling policies where it is used as warm-up. Then, we perform empirical studies in four real world datasets, with various magnitudes of class imbalance. The results show that our method can more quickly reach a high performance model than standard AL policies. Its observed gains over random sampling can reach 80% and be competitive with policies with an unlimited annotation budget or additional historical data (with 1/10 to 1/50 of the labels).