Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior distributions. For this purpose, Monte Carlo (MC) methods, such as Markov Chain Monte Carlo and importance sampling algorithms, are often employed. In this work, we introduce the theory and practice of a Compressed MC (C-MC) scheme to compress the statistical information contained in a set of random samples. In its basic version, C-MC is strictly related to the stratification technique, a well-known method used for variance reduction purposes. Deterministic C-MC schemes are also presented, which provide very good performance. The compression problem is strictly related to the moment matching approach applied in different filtering techniques, usually called as Gaussian quadrature rules or sigma-point methods. C-MC can be employed in a distributed Bayesian inference framework when cheap and fast communications with a central processor are required. Furthermore, C-MC is useful within particle filtering and adaptive IS algorithms, as shown by three novel schemes introduced in this work. Six numerical results confirm the benefits of the introduced schemes, outperforming the corresponding benchmark methods. A related code is also provided.

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.

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.

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).

Causal discovery automates the learning of causal Bayesian networks from data and has been of active interest from their beginning. With the sourcing of large data sets off the internet, interest in scaling up to very large data sets has grown. One approach to this is to parallelize search using Markov Blanket (MB) discovery as a first step, followed by a process of combining MBs in a global causal model. We develop and explore three new methods of MB discovery using Minimum Message Length (MML) and compare them empirically to the best existing methods, whether developed specifically as MB discovery or as feature selection. Our best MML method is consistently competitive and has some advantageous features.

Natural Language Processing (NLP) systems have been subjected to a Cambrian explosion of architectural paradigms in the past few years. The scale on the number of contributions and its exponential growth, bring challenges in understanding how NLP architectural patterns evolve and consolidate in different sub-areas and tasks. This paper aims to provide the methodological support for the interpretation of NLP architectural patterns at scale by applying statistical corpus analysis methods over large-scale NLP corpora. We analyse the use of corpus statistics to compute large-scale collocation patterns jointly with graph visualisation methods as a device to interpret architectural patterns at scale. The proposed methods aims to address questions such as: - What is the complete list of architectural patterns present in NLP? - What are the prevailing architectural patterns (classifiers, layers, regularisation, linguistic resources) for each NLP task? - How these patterns are evolving over time and what are the emerging consolidated/canonical architectural motifs?

By 2035 AI could boost average profitability rates by 38 percent and lead to an economic increase of $14 Trillion. The words Artificial Intelligence (AI), and algorithms are most often misused and misunderstood. There are often used interchangeably when they shouldn't be. This leads to unnecessary confusion. In this article, let's understand what AI and algorithms are, and what the difference between them is.