Maximum Likelihood Estimation (MLE) is a probabilistic based approach to determine values for the parameters of the model. Parameters could be defined as blueprints for the model because based on that the algorithm works. MLE is a widely used technique in machine learning, time series, panel data and discrete data. The motive of MLE is to maximize the likelihood of values for the parameter to get the desired outcomes. Following are the topics to be covered.

Machine Learning and Artificial Intelligence have been deemed the "hot topics" for every trending article in 2021. It's similar to how the internet revolutionized everyone's lives. Artificial Intelligence (A.I.) and Machine Learning will transform our lives in ways labelled impossible years ago. In 1959, Arthur Samuel coined the term Machine Learning. He was a pioneer in Artificial Intelligence, computer gaming and Machine Learning.

The Naive Bayes algorithm is a classification technique that is based on the Bayes' Theorem. It assumes that the predictors are independent of each other. A Naive Bayes classifier assumes that the presence of a certain feature in a class is not related to the presence of any other feature. For example, the apple fruit is characterized by red color, round shape, and about 3 inches of diameter. Although these features depend on each other, they independently contribute to the probability of the fruit being an apple.

Predictive process monitoring is an exceedingly active field of research. At its core, the fundamental component of predictive monitoring is the abstraction technique it uses to obtain a fixed-length representation of the process component subject to the prediction (often, but not always, process traces). In the earlier approaches, the need for such abstraction was overcome through model-aware techniques, employing process models and replay techniques on partial traces to abstract a flat representation of event sequences. Such process models are mostly automatically discovered from a set of available complete traces, and require perfect fitness on training instances (and, seldomly, also on unseen test instances). For instance, van der Aalst et al. [van_der_aalst_time_2011] proposed a time prediction framework based on replaying partial traces on a transition system, effectively clustering training instances by control-flow information.

We propose a framework for the statistical evaluation of variational auto-encoders (VAEs) and test two instances of this framework in the context of modelling images of handwritten digits and a corpus of English text. Our take on evaluation is based on the idea of statistical model criticism, popular in Bayesian data analysis, whereby a statistical model is evaluated in terms of its ability to reproduce statistics of an unknown data generating process from which we can obtain samples. A VAE learns not one, but two joint distributions over a shared sample space, each exploiting a choice of factorisation that makes sampling tractable in one of two directions (latent-to-data, data-to-latent). We evaluate samples from these distributions, assessing their (marginal) fit to the observed data and our choice of prior, and we also evaluate samples through a pipeline that connects the two distributions starting from a data sample, assessing whether together they exploit and reveal latent factors of variation that are useful to a practitioner. We show that this methodology offers possibilities for model selection qualitatively beyond intrinsic evaluation metrics and at a finer granularity than commonly used statistics can offer.

In this paper we propose Discretely Indexed flows (DIF) as a new tool for solving variational estimation problems. Roughly speaking, DIF are built as an extension of Normalizing Flows (NF), in which the deterministic transport becomes stochastic, and more precisely discretely indexed. Due to the discrete nature of the underlying additional latent variable, DIF inherit the good computational behavior of NF: they benefit from both a tractable density as well as a straightforward sampling scheme, and can thus be used for the dual problems of Variational Inference (VI) and of Variational density estimation (VDE). On the other hand, DIF can also be understood as an extension of mixture density models, in which the constant mixture weights are replaced by flexible functions. As a consequence, DIF are better suited for capturing distributions with discontinuities, sharp edges and fine details, which is a main advantage of this construction. Finally we propose a methodology for constructiong DIF in practice, and see that DIF can be sequentially cascaded, and cascaded with NF.

The deep learning revolution incited by the 2012 Alexnet paper has been transformative for the field of computer vision. Many problems which were severely limited using classical solutions are now seeing unprecedented success. The rapid proliferation of deep learning methods has led to a sharp increase in their use in consumer and embedded applications. One consequence of consumer and embedded applications is lossy multimedia compression which is required to engineer the efficient storage and transmission of data in these real-world scenarios. As such, there has been increased interest in a deep learning solution for multimedia compression which would allow for higher compression ratios and increased visual quality. The deep learning approach to multimedia compression, so called Learned Multimedia Compression, involves computing a compressed representation of an image or video using a deep network for the encoder and the decoder. While these techniques have enjoyed impressive academic success, their industry adoption has been essentially non-existent. Classical compression techniques like JPEG and MPEG are too entrenched in modern computing to be easily replaced. This dissertation takes an orthogonal approach and leverages deep learning to improve the compression fidelity of these classical algorithms. This allows the incredible advances in deep learning to be used for multimedia compression without threatening the ubiquity of the classical methods. The key insight of this work is that methods which are motivated by first principles, i.e., the underlying engineering decisions that were made when the compression algorithms were developed, are more effective than general methods. By encoding prior knowledge into the design of the algorithm, the flexibility, performance, and/or accuracy are improved at the cost of generality...

We present a unified probabilistic gradient boosting framework for regression tasks that models and predicts the entire conditional distribution of a univariate response variable as a function of covariates. Our likelihood-based approach allows us to either model all conditional moments of a parametric distribution, or to approximate the conditional cumulative distribution function via Normalizing Flows. As underlying computational backbones, our framework is based on XGBoost and LightGBM. Modelling and predicting the entire conditional distribution greatly enhances existing tree-based gradient boosting implementations, as it allows to create probabilistic forecasts from which prediction intervals and quantiles of interest can be derived. Empirical results show that our framework achieves state-of-the-art forecast accuracy.

The combinatorial search space presents a significant challenge to learning causality from data. Recently, the problem has been formulated into a continuous optimization framework with an acyclicity constraint, allowing for the exploration of deep generative models to better capture data sample distributions and support the discovery of Directed Acyclic Graphs (DAGs) that faithfully represent the underlying data distribution. However, so far no study has investigated the use of Wasserstein distance for causal structure learning via generative models. This paper proposes a new model named DAG-WGAN, which combines the Wasserstein-based adversarial loss, an auto-encoder architecture together with an acyclicity constraint. DAG-WGAN simultaneously learns causal structures and improves its data generation capability by leveraging the strength from the Wasserstein distance metric. Compared with other models, it scales well and handles both continuous and discrete data. Our experiments have evaluated DAG-WGAN against the state-of-the-art and demonstrated its good performance. Causal discovery involves the process of learning structures of Bayesian Networks (BN) from data.

In 1958, the New York Times reported on a new machine called the perceptron. Frank Rosenblatt, its inventor, demonstrated that the perceptron was able to learn from experience. He predicted that later perceptrons would be able to recognize people, or instantly translate spoken language. Now a reality, this must have sounded like distant science fiction at the time. In hindsight, we may consider it the birth of machine learning, the field fueling most of the current advances in artificial intelligence (AI). Around the same time, another equally revolutionary development took place: scientists understood that computers could do more than compute numbers: they can process symbols. Although this insight was also motivated by artificial intelligence, in hindsight it was the birth of the field of computer science. There was great optimism that the manipulation of symbols, in programs written by humans, implementing rules designed by humans, should be enough to generate intelligence. Below, we shall refer to this as the symbol-rule hypothesis.