Finding a good way to model probability densities is key to probabilistic inference. An ideal model should be able to concisely approximate any probability, while being also compatible with two main operations: multiplications of two models (product rule) and marginalization with respect to a subset of the random variables (sum rule). In this work, we show that a recently proposed class of positive semi-definite (PSD) models for non-negative functions is particularly suited to this end. In particular, we characterize both approximation and generalization capabilities of PSD models, showing that they enjoy strong theoretical guarantees. Moreover, we show that we can perform efficiently both sum and product rule in closed form via matrix operations, enjoying the same versatility of mixture models. Our results open the way to applications of PSD models to density estimation, decision theory and inference. Preliminary empirical evaluation supports our findings.

Twenty-three machine learning algorithms were trained then scored to establish baseline comparison metrics and to select an image classification algorithm worthy of embedding into mission-critical satellite imaging systems. The Overhead-MNIST dataset is a collection of satellite images similar in style to the ubiquitous MNIST hand-written digits found in the machine learning literature. The CatBoost classifier, Light Gradient Boosting Machine, and Extreme Gradient Boosting models produced the highest accuracies, Areas Under the Curve (AUC), and F1 scores in a PyCaret general comparison. Separate evaluations showed that a deep convolutional architecture was the most promising. We present results for the overall best performing algorithm as a baseline for edge deployability and future performance improvement: a convolutional neural network (CNN) scoring 0.965 categorical accuracy on unseen test data.

Promising results were obtained with the gradient boosting classifier. Predicting the success of a business venture has always been a struggle for both practitioners and researchers. However, thanks to companies that aggregate data about other firms, it has become possible to create and validate predictive models based on an unprecedented amount of real-world examples. In this study, we use data obtained from one of the largest platforms integrating business information – Crunchbase. Our final training set consisted of 213 171 companies.

"Logistic Regression is not Regression but a Classification Algorithm". You might have seen this in latest popular machine learning books, blogs or you might have heard *Data Science Gurus* utter the same in their highly subscribed YouTube channels. Machine learning has usurped and renamed many statistical techniques. Often to the extent that they now disbelieve and reject its statistical origins. Case in point is "Logistic regression is not Regression" However, nothing can be further from the truth than this assertion.

This Course Organisations all around the world are using data to predict behaviours and extract valuable real-world insights to inform decisions. Managing and analysing big data has become an essential part of modern finance, retail, marketing, social science, development and research, medicine and government. This MOOC, designed by an academic team from Goldsmiths, University of London, will quickly introduce you to the core concepts of Data Science to prepare you for intermediate and advanced Data Science courses. It focuses on the basic mathematics, statistics and programming skills that are necessary for typical data analysis tasks. You will consider these fundamental concepts on an example data clustering task, and you will use this example to learn basic programming skills that are necessary for mastering Data Science techniques.

As a beginner, you want to know what are the models and algorithms available in machine learning that make our work more easier. Supervised learning involves learning a function that maps an input to an output based on example input-output pairs. In regression models, the output is continuous. The idea of linear regression is simply finding a line that best fits the data. Extensions of linear regression include multiple linear regression.

This can be naturally modeled constantly explore innovative ways to provide optimal online as contextual bandit problems (e.g., LinUCB [18] and Thompson user experiences for gaining competitive advantages. The great sampling [7]), where each arm corresponds to an item, pulling an needs of developing intelligent interactive recommendation systems item indicates recommending an item, and the reward is the instant are indicated, which could sequentially suggest users the most feedback from a user after the recommendation. Contextual proper items by accurately predicting their preferences, while receiving bandit algorithms have been widely applied in various interactive the up-to-date feedback to refine the recommendation results, recommender systems by achieving an optimal tradeoff between continuosly. Multi-armed bandit algorithms, which have been exploration and exploitation. Based on the preliminary studies [15, widely applied into various online systems, are quite capable of 18, 1], several practical challenges are identified in modern recommender delivering such efficient recommendation services.

Botnets are one of the online threats with the biggest presence, causing billionaire losses to global economies. Nowadays, the increasing number of devices connected to the Internet makes it necessary to analyze large amounts of network traffic data. In this work, we focus on increasing the performance on botnet traffic classification by selecting those features that further increase the detection rate. For this purpose we use two feature selection techniques, Information Gain and Gini Importance, which led to three pre-selected subsets of five, six and seven features. Then, we evaluate the three feature subsets along with three models, Decision Tree, Random Forest and k-Nearest Neighbors. To test the performance of the three feature vectors and the three models we generate two datasets based on the CTU-13 dataset, namely QB-CTU13 and EQB-CTU13. We measure the performance as the macro averaged F1 score over the computational time required to classify a sample. The results show that the highest performance is achieved by Decision Trees using a five feature set which obtained a mean F1 score of 85% classifying each sample in an average time of 0.78 microseconds.

In this thesis, we explore and apply methods inspired by the free energy principle to two important areas in machine learning and neuroscience. The free energy principle is a general mathematical theory of the necessary information-theoretic behaviours of systems which maintain a separation from their environment. A core postulate of the theory is that complex systems can be seen as performing variational Bayesian inference and minimizing an information-theoretic quantity called the variational free energy. The free energy principle originated in, and has been extremely influential in theoretical neuroscience, having spawned a number of neurophysiologically realistic process theories, and maintaining close links with Bayesian Brain viewpoints. The thesis is split into three main parts where we apply methods and insights from the free energy principle to understand questions first in perception, then action, and finally learning. Specifically, in the first section, we focus on the theory of predictive coding, a neurobiologically plausible process theory derived from the free energy principle under certain assumptions, which argues that the primary function of the brain is to minimize prediction errors. We focus on scaling up predictive coding architectures and simulate large-scale predictive coding networks for perception on machine learning benchmarks; we investigate predictive coding's relationship to other classical filtering algorithms, and we demonstrate that many biologically implausible aspects of current models of predictive coding can be relaxed without unduly harming the performance of predictive coding models which allows for a potentially more literal translation of predictive coding theory into cortical microcircuits. In the second part of the thesis, we focus on the application of methods deriving from the free energy principle to action. We study the extension of methods of'active inference', a neurobiologically grounded account of action through variational message passing, to utilize deep artificial neural networks, allowing these methods to'scale up' to be competitive with state of the art deep reinforcement learning methods.

We leverage state-of-the-art machine learning methods and a decade's worth of archival data from the Canada-France-Hawaii Telescope (CFHT) to predict observatory image quality (IQ) from environmental conditions and observatory operating parameters. Specifically, we develop accurate and interpretable models of the complex dependence between data features and observed IQ for CFHT's wide field camera, MegaCam. Our contributions are several-fold. First, we collect, collate and reprocess several disparate data sets gathered by CFHT scientists. Second, we predict probability distribution functions (PDFs) of IQ, and achieve a mean absolute error of $\sim0.07''$ for the predicted medians. Third, we explore data-driven actuation of the 12 dome ``vents'', installed in 2013-14 to accelerate the flushing of hot air from the dome. We leverage epistemic and aleatoric uncertainties in conjunction with probabilistic generative modeling to identify candidate vent adjustments that are in-distribution (ID) and, for the optimal configuration for each ID sample, we predict the reduction in required observing time to achieve a fixed SNR. On average, the reduction is $\sim15\%$. Finally, we rank sensor data features by Shapley values to identify the most predictive variables for each observation. Our long-term goal is to construct reliable and real-time models that can forecast optimal observatory operating parameters for optimization of IQ. Such forecasts can then be fed into scheduling protocols and predictive maintenance routines. We anticipate that such approaches will become standard in automating observatory operations and maintenance by the time CFHT's successor, the Maunakea Spectroscopic Explorer (MSE), is installed in the next decade.