Artificial Intelligence has come a long way from being the stuff of science fiction movies and books to becoming an integral part of our daily lives. Today, AI is one of the fastest growing global industries. Investments and experiments in AI have been taking place all around the world. Given its unimaginably wide range of uses; AI is a field of expertise that is set to grow in a very huge way over the coming years. AI professionals are among the highest paid in the field of IT. Ans: Artificial Intelligence is a part of computer science that aims to create machine that are intelligent and seek to work and react the way humans do. Q2)What to you understand by an artificial intelligence Neural Network?

Belief propagation is a fundamental message-passing algorithm for probabilistic reasoning and inference in graphical models. While it is known to be exact on trees, in most applications belief propagation is run on graphs with cycles. Understanding the behavior of "loopy" belief propagation has been a major challenge for researchers in machine learning, and positive convergence results for BP are known under strong assumptions which imply the underlying graphical model exhibits decay of correlations. We show that under a natural initialization, BP converges quickly to the global optimum of the Bethe free energy for Ising models on arbitrary graphs, as long as the Ising model is \emph{ferromagnetic} (i.e. neighbors prefer to be aligned). This holds even though such models can exhibit long range correlations and may have multiple suboptimal BP fixed points. We also show an analogous result for iterating the (naive) mean-field equations; perhaps surprisingly, both results are dimension-free in the sense that a constant number of iterations already provides a good estimate to the Bethe/mean-field free energy.

A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte Carlo methods. We propose a new sampling algorithm based on a birth-death mechanism to accelerate the mixing of Langevin diffusion. Our algorithm is motivated by its mean field partial differential equation (PDE), which is a Fokker-Planck equation supplemented by a nonlocal birth-death term. This PDE can be viewed as a gradient flow of the Kullback-Leibler divergence with respect to the Wasserstein-Fisher-Rao metric. We prove that under some assumptions the asymptotic convergence rate of the nonlocal PDE is independent of the potential barrier, in contrast to the exponential dependence in the case of the Langevin diffusion. We illustrate the efficiency of the birth-death accelerated Langevin method through several analytical examples and numerical experiments.

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for modeling real-valued nonlinear functions due to their flexibility and uncertainty quantification. However, the typical GP regression model suffers from several drawbacks: i) Conventional GP inference scales $O(N^{3})$ with respect to the number of observations; ii) updating a GP model sequentially is not trivial; and iii) covariance kernels often enforce stationarity constraints on the function, while GPs with non-stationary covariance kernels are often intractable to use in practice. To overcome these issues, we propose an online sequential Monte Carlo algorithm to fit mixtures of GPs that capture non-stationary behavior while allowing for fast, distributed inference. By formulating hyperparameter optimization as a multi-armed bandit problem, we accelerate mixing for real time inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the context of prediction for simulated non-stationary data and hospital time series data.

ABSTRACT-An investigation of deep fuzzy systems is presented in this paper. A deep fuzzy system is represented by recursive fuzzy systems from an input terminal to output terminal. Recursive fuzzy systems are sequences of fuzzy grade memberships obtained using fuzzy transmition functions and recursive calls to fuzzy systems. A recursive fuzzy system which calls a fuzzy system times includes fuzzy chains to evaluate the final grade membership of this recursive system. A connection matrix which includes recursive calls are used to represent recursive fuzzy systems.

Many algorithms for score-based Bayesian network structure learning (BNSL) take as input a collection of potentially optimal parent sets for each variable in a data set. Constructing these collections naively is computationally intensive since the number of parent sets grows exponentially with the number of variables. Therefore, pruning techniques are not only desirable but essential. While effective pruning exists for the Bayesian Information Criterion (BIC), current results for the Bayesian Dirichlet equivalent uniform (BDeu) score reduce the search space very modestly, hampering the use of (the often preferred) BDeu. We derive new non-trivial theoretical upper bounds for the BDeu score that considerably improve on the state of the art. Since the new bounds are efficient and easy to implement, they can be promptly integrated into many BNSL methods. We show that gains can be significant in multiple UCI data sets so as to highlight practical implications of the theoretical advances.

Generative Adversarial Networks (GANs) enjoy great success at image generation, but have proven difficult to train in the domain of natural language. Challenges with gradient estimation, optimization instability, and mode collapse have lead practitioners to resort to maximum likelihood pre-training, followed by small amounts of adversarial fine-tuning. The benefits of GAN fine-tuning for language generation are unclear, as the resulting models produce comparable or worse samples than traditional language models. We show it is in fact possible to train a language GAN from scratch -- without maximum likelihood pre-training. We combine existing techniques such as large batch sizes, dense rewards and discriminator regularization to stabilize and improve language GANs. The resulting model, ScratchGAN, performs comparably to maximum likelihood training on EMNLP2017 News and WikiText-103 corpora according to quality and diversity metrics.

Resampling techniques are widely used in statistical inference and ensemble learning, in which estimators' statistical properties are essential. However, existing methods are computationally demanding, because repetitions of estimation/learning via numerical optimization/integral for each resampled data are required. In this study, we introduce a computationally efficient method to resolve such problem: replicated vector approximate message passing. This is based on a combination of the replica method of statistical physics and an accurate approximate inference algorithm, namely the vector approximate message passing of information theory. The method provides tractable densities without repeating estimation/learning, and the densities approximately offer an arbitrary degree of the estimators' moment in practical time. In the experiment, we apply the proposed method to the stability selection method, which is commonly used in variable selection problems. The numerical results show its fast convergence and high approximation accuracy for problems involving both synthetic and real-world datasets.

In this paper, an issue of building the RRC model using probability distributions other than beta distribution is addressed. More precisely, in this paper, we propose to build the RRR model using the truncated normal distribution. Heuristic procedures for expected value and the variance of the truncated-normal distribution are also proposed. The proposed approach is tested using SCM-based model for testing the consequences of applying the truncated normal distribution in the RRC model. The experimental evaluation is performed using four different base classifiers and seven quality measures. The results showed that the proposed approach is comparable to the RRC model built using beta distribution. What is more, for some base classifiers, the truncated-normal-based SCM algorithm turned out to be better at discovering objects coming from minority classes.

Performing exact Bayesian inference for complex models is intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable approximations of the posterior distribution but are computationally expensive for large datasets. A standard approach to mitigate this complexity consists of using subsampling techniques or distributing the data across a cluster. However, these approaches are typically unreliable in high-dimensional scenarios. We focus here on an alternative class of MCMC schemes exploiting a splitting strategy akin to the one used by the celebrated ADMM optimization algorithm. These methods, proposed recently in [43, 51], appear to provide empirically state-of-the-art performance. We generalize here these ideas and propose a detailed theoretical study of one of these algorithms known as the Split Gibbs Sampler. Under regularity conditions, we establish explicit dimension-free convergence rates for this scheme using Ricci curvature and coupling ideas. We demonstrate experimentally the excellent performance of these MCMC schemes on various applications.