To model high dimensional data, Gaussian methods are widely used since they remain tractable and yield parsimonious models by imposing strong assumptions on the data. Vine copulas are more flexible by combining arbitrary marginal distributions and (conditional) bivariate copulas. Yet, this adaptability is accompanied by sharply increasing computational effort as the dimension increases. The approach proposed in this paper overcomes this burden and makes the first step into ultra high dimensional non-Gaussian dependence modeling by using a divide-and-conquer approach. First, we apply Gaussian methods to split datasets into feasibly small subsets and second, apply parsimonious and flexible vine copulas thereon. Finally, we reconcile them into one joint model. We provide numerical results demonstrating the feasibility of our approach in moderate dimensions and showcase its ability to estimate ultra high dimensional non-Gaussian dependence models in thousands of dimensions.

Here's a situation you've got into: You are working on a classification problem and you have generated your set of hypothesis, created features and discussed the importance of variables. Within an hour, stakeholders want to see the first cut of the model. You have hunderds of thousands of data points and quite a few variables in your training data set. In such situation, if I were at your place, I would have used'Naive Bayes', which can be extremely fast relative to other classification algorithms. It works on Bayes theorem of probability to predict the class of unknown data set.

Most of the beginners start by learning regression. It is simple to learn and use, but does that solve our purpose? Because, you can do so much more than just Regression! Think of machine learning algorithms as an armory packed with axes, sword, blades, bow, dagger etc. You have various tools, but you ought to learn to use them at the right time.

For many people, the concept of Artificial Intelligence (AI) is a thing of the future. It is the technology that is yet to be introduced. But Professor Jon Oberlander disagrees. He was quick to point out that AI is not in the future, it is now in the making. He began by mentioning Alexa, Amazon's star product. It's an artificial intelligent personal assistant, which was made popular by Amazon Echo devices.

We consider the problem of sequentially making decisions that are rewarded by "successes" and "failures" which can be predicted through an unknown relationship that depends on a partially controllable vector of attributes for each instance. The learner takes an active role in selecting samples from the instance pool. The goal is to maximize the probability of success in either offline (training) or online (testing) phases. Our problem is motivated by real-world applications where observations are time-consuming and/or expensive. We develop a knowledge gradient policy using an online Bayesian linear classifier to guide the experiment by maximizing the expected value of information of labeling each alternative. We provide a finite-time analysis of the estimated error and show that the maximum likelihood estimator based produced by the KG policy is consistent and asymptotically normal. We also show that the knowledge gradient policy is asymptotically optimal in an offline setting. This work further extends the knowledge gradient to the setting of contextual bandits. We report the results of a series of experiments that demonstrate its efficiency.

In this paper, we consider the use of structure learning methods for probabilistic graphical models to identify statistical dependencies in high-dimensional physical processes. Such processes are often synthetically characterized using PDEs (partial differential equations) and are observed in a variety of natural phenomena, including geoscience data capturing atmospheric and hydrological phenomena. Classical structure learning approaches such as the PC algorithm and variants are challenging to apply due to their high computational and sample requirements. Modern approaches, often based on sparse regression and variants, do come with finite sample guarantees, but are usually highly sensitive to the choice of hyper-parameters, e.g., parameter $\lambda$ for sparsity inducing constraint or regularization. In this paper, we present ACLIME-ADMM, an efficient two-step algorithm for adaptive structure learning, which estimates an edge specific parameter $\lambda_{ij}$ in the first step, and uses these parameters to learn the structure in the second step. Both steps of our algorithm use (inexact) ADMM to solve suitable linear programs, and all iterations can be done in closed form in an efficient block parallel manner. We compare ACLIME-ADMM with baselines on both synthetic data simulated by partial differential equations (PDEs) that model advection-diffusion processes, and real data (50 years) of daily global geopotential heights to study information flow in the atmosphere. ACLIME-ADMM is shown to be efficient, stable, and competitive, usually better than the baselines especially on difficult problems. On real data, ACLIME-ADMM recovers the underlying structure of global atmospheric circulation, including switches in wind directions at the equator and tropics entirely from the data.

Brain-Computer Interface (BCI) uses brain signals in order to provide a new method for communication between human and outside world. Feature extraction, selection and classification are among the main matters of concerns in signal processing stage of BCI. In this article, we present our findings about the most effective features and classifiers in some brain tasks. Six different groups of classical features and twelve classifiers have been examined in nine datasets of brain signal. The results indicate that energy of brain signals in {\alpha} and \b{eta} frequency bands, together with some statistical parameters are more effective, comparing to the other types of extracted features. In addition, Bayesian classifier with Gaussian distribution assumption and also Support Vector Machine (SVM) show to classify different BCI datasets more accurately than the other classifiers. We believe that the results can give an insight about a strategy for blind classification of brain signals in brain-computer interface.

In this paper we present a comprehensive view of prominent causal discovery algorithms, categorized into two main categories (1) assuming acyclic and no latent variables, and (2) allowing both cycles and latent variables, along with experimental results comparing them from three perspectives: (a) structural accuracy, (b) standard predictive accuracy, and (c) accuracy of counterfactual inference. For (b) and (c) we train causal Bayesian networks with structures as predicted by each causal discovery technique to carry out counterfactual or standard predictive inference. We compare causal algorithms on two pub- licly available and one simulated datasets having different sample sizes: small, medium and large. Experiments show that structural accuracy of a technique does not necessarily correlate with higher accuracy of inferencing tasks. Fur- ther, surveyed structure learning algorithms do not perform well in terms of structural accuracy in case of datasets having large number of variables.

Sampling is a fundamental topic in graph signal processing, having found applications in estimation, clustering, and video compression. In contrast to traditional signal processing, the irregularity of the signal domain makes selecting a sampling set non-trivial and hard to analyze. Indeed, though conditions for graph signal interpolation from noiseless samples exist, they do not lead to a unique sampling set. The presence of noise makes choosing among these sampling sets a hard combinatorial problem. Although greedy sampling schemes are commonly used in practice, they have no performance guarantee. This work takes a twofold approach to address this issue. First, universal performance bounds are derived for the Bayesian estimation of graph signals from noisy samples. In contrast to currently available bounds, they are not restricted to specific sampling schemes and hold for any sampling sets. Second, this paper provides near-optimal guarantees for greedy sampling by introducing the concept of approximate submodularity and updating the classical greedy bound. It then provides explicit bounds on the approximate supermodularity of the interpolation mean-square error showing that it can be optimized with worst-case guarantees using greedy search even though it is not supermodular. Simulations illustrate the derived bound for different graph models and show an application of graph signal sampling to reduce the complexity of kernel principal component analysis.

Looking at the picture above you may have easily figured out \(P(\text{red} \text{yellow})\) by thinking "This is easy! There are 6 yellow pegs, 4 of them are over red so the probability of being over a red block if I'm on a yellow one is 4/6". If you did follow this line of thinking congratulations, you just independently discovered Bayes' Theorem! Of course mathematical language is extremely concise, and human intuition is able to easily jump steps in its reasoning process; getting from our intuition to Bayes' Theorem will require a bit of work. Let's begin formalizing this intuition by coming up with a way to calculate "there are 6 yellow pegs."