Machine Learning Algorithms – DataScientist may be the sexiest job of today but the understanding, implementation, applied ML experience is missing. Having the top algorithms on your fingertips in real business is missing big time. The real job for any data scientist is the ability to clarify, demonstrate, extract real values out of data and reap rewards. "Machine Learning" as a basic skill sounds like teleportation tool to many businesses especially for the companies which are actually data factories i.e social media platforms. Describing and picturising the top few machine learning algorithms is the main idea of this post.

I'm following the book Pattern recognition and machine learning by Bishop on Bernoulli mixture model, and trying to code it. But I don't understand how to calculate the conditional probability (page 446 of the first edition) So in the E-step I'm supposed to calculate this. But it is said that we should use the log of the probability, so as to avoid numerical underflow. So how do i apply it here? I can't see any way to do it.

The derivation of physical laws is a dominant topic in scientific research. We propose a new method capable of discovering the physical laws from data to tackle four challenges in the previous methods. The four challenges are: (1) large noise in the data, (2) outliers in the data, (3) integrating the data collected from different experiments, and (4) extrapolating the solutions to the areas that have no available data. To resolve these four challenges, we try to discover the governing differential equations and develop a model-discovering method based on sparse Bayesian inference and subsampling. The subsampling technique is used for improving the accuracy of the Bayesian learning algorithm here, while it is usually employed for estimating statistics or speeding up algorithms elsewhere. The optimal subsampling size is moderate, neither too small nor too big. Another merit of our method is that it can work with limited data by the virtue of Bayesian inference. We demonstrate how to use our method to tackle the four aforementioned challenges step by step through numerical examples: (1) predator-prey model with noise, (2) shallow water equations with outliers, (3) heat diffusion with random initial and boundary conditions, and (4) fish-harvesting problem with bifurcations. Numerical results show that the robustness and accuracy of our new method is significantly better than the other model-discovering methods and traditional regression methods.

Owe to the recent advancements in Artificial Intelligence especially deep learning, many data-driven decision support systems have been implemented to facilitate medical doctors in delivering personalized care. We focus on the deep reinforcement learning (DRL) models in this paper. DRL models have demonstrated human-level or even superior performance in the tasks of computer vision and game playings, such as Go and Atari game. However, the adoption of deep reinforcement learning techniques in clinical decision optimization is still rare. We here present the first survey that summarizes reinforcement learning algorithms with Deep Neural Networks (DNN) on clinical decision support. We also discuss some case studies, where different DRL algorithms were applied to address various clinical challenges. We further compare and contrast the advantages and limitations of various DRL algorithms and present a preliminary guide on how to choose the appropriate DRL algorithm for particular clinical applications.

Real-world optimization problems typically involve multiple objectives. This is particularly true in the design of engineering systems, where multiple performance outcomes are balanced against budgetary constraints. Among the complexities of optimizing over multiple objectives is the effect of uncertainties in the problem. Design is guided by models known to be imperfect, systems are built using materials with uncertainty regarding their properties, variations occur in the construction of designed systems, and so on. These imperfections, uncertainties and errors cause uncertainty also in the solution to a design problem. In traditional engineering design, one designs a system after choosing a material with appropriate properties for the project from a database of known materials. As a result, the design of the system is constrained by the initial material selection. By coupling material discovery and engineering system design, we can combine these two traditionally separate processes under the umbrella of a unified multiple objective optimization problem. In this paper, we cast the engineering design problem in the framework of computer model calibration.

The main motivation of this work was practical, to offer computationally and theoretical scalable ways to structuring large classes of computation. It started from attempts to optimize R code for machine learning/artificial intelligence algorithms for huge data sets, that due to their size, should be handled into an incremental (online) fashion. Our target are large classes of relational (attribute based), mathematical (index based) or graph computations. We wanted to use powerful computation representations that emerged in AI (artificial intelligence)/ML (machine learning) as BN (Bayesian networks) and CNN (convolution neural networks). For the classes of computation addressed by us, and for our HPC (high performance computing) needs, the current solutions for translating computations into such representation need to be extended. Our results show that the classes of computation targeted by us, could be tree-structured, and a probability distribution (defining a DBN, i.e. Dynamic Bayesian Network) associated with it. More ever, this DBN may be viewed as a recursive CNN (Convolution Neural Network). Within this tree-like structure, classification in classes with size bounded (by a parameterizable may be performed. These results are at the core of very powerful, yet highly practically algorithms for restructuring and parallelizing the computations. The mathematical background required for an in depth presentation and exposing the full generality of our approach) is the subject of a subsequent paper. In this paper, we work in an limited (but important) framework that could be understood with rudiments of linear algebra and graph theory. The focus is in applicability, most of this paper discuss the usefulness of our approach for solving hard compilation problems related to automatic parallelism.

To speed up convergence a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation Maximization (MCMC-SAEM) algorithm for general latent variable models is proposed. For exponential models the algorithm is shown to be convergent under classical conditions as the number of iterations increases. Numerical experiments illustrate the performance of the mini-batch algorithm in various models. In particular, we highlight that an appropriate choice of the mini-batch size results in a tremendous speed-up of the convergence of the sequence of estimators generated by the algorithm. Moreover, insights on the effect of the mini-batch size on the limit distribution are presented.

Bayesian inference is used extensively to infer and to quantify the uncertainty in a field of interest from a measurement of a related field when the two are linked by a physical model. Despite its many applications, Bayesian inference faces challenges when inferring fields that have discrete representations of large dimension, and/or have prior distributions that are difficult to represent mathematically. In this manuscript we consider the use of Generative Adversarial Networks (GANs) in addressing these challenges. A GAN is a type of deep neural network equipped with the ability to learn the distribution implied by multiple samples of a given field. Once trained on these samples, the generator component of a GAN maps the iid components of a low-dimensional latent vector to an approximation of the distribution of the field of interest. In this work we demonstrate how this approximate distribution may be used as a prior in a Bayesian update, and how it addresses the challenges associated with characterizing complex prior distributions and the large dimension of the inferred field. We demonstrate the efficacy of this approach by applying it to the problem of inferring and quantifying uncertainty in the initial temperature field in a heat conduction problem from a noisy measurement of the temperature at later time.

Matrix-variate distributions can intuitively model the dependence structure of matrix-valued observations that arise in applications with multivariate time series, spatio-temporal or repeated measures. This paper develops an Expectation-Maximization algorithm for discriminant analysis and classification with matrix-variate $t$-distributions. The methodology shows promise on simulated datasets or when applied to the forensic matching of fractured surfaces or the classification of functional Magnetic Resonance, satellite or hand gestures images.

A Markov Decision Process (MDP) is a popular model for reinforcement learning. However, its commonly used assumption of stationary dynamics and rewards is too stringent and fails to hold in adversarial, nonstationary, or multi-agent problems. We study an episodic setting where the parameters of an MDP can differ across episodes. We learn a reliable policy of this potentially adversarial MDP by developing an Adversarial Reinforcement Learning (ARL) algorithm that reduces our MDP to a sequence of \emph{adversarial} bandit problems. ARL achieves $O(\sqrt{SATH^3})$ regret, which is optimal with respect to $S$, $A$, and $T$, and its dependence on $H$ is the best (even for the usual stationary MDP) among existing model-free methods.