The following is an unsupervised machine-learning algorithm that recognizes and predicts input patterns in real-time. The algorithm is essentially a system of information-processing inspired by the cognitive functions of the mind. The system has a collection of interacting memory systems akin to the spychological concepts of short-term and long-term memory, which allows it to learn by observation and adapt based on the frequency of patterns and their relationships through time. An association value is a representation of conditional probability which is calculated between the current observation and the rest of the elements in the buffer, i.e. the previous N observations, then stored in the association matrix. Each elements current place in the buffer determines the strength of the delta applied to its association value, so more recent observation are more strongly associated with the current observations than those further in the buffer.

In this work, we propose an infinite restricted Boltzmann machine (RBM), whose maximum likelihood estimation (MLE) corresponds to a constrained convex optimization. We consider the Frank-Wolfe algorithm to solve the program, which provides a sparse solution that can be interpreted as inserting a hidden unit at each iteration, so that the optimization process takes the form of a sequence of finite models of increasing complexity. As a side benefit, this can be used to easily and efficiently identify an appropriate number of hidden units during the optimization. The resulting model can also be used as an initialization for typical state-of-the-art RBM training algorithms such as contrastive divergence, leading to models with consistently higher test likelihood than random initialization.

The infinite restricted Boltzmann machine (iRBM) is an extension of the classic RBM. It enjoys a good property of automatically deciding the size of the hidden layer according to specific training data. With sufficient training, the iRBM can achieve a competitive performance with that of the classic RBM. However, the convergence of learning the iRBM is slow, due to the fact that the iRBM is sensitive to the ordering of its hidden units, the learned filters change slowly from the left-most hidden unit to right. To break this dependency between neighboring hidden units and speed up the convergence of training, a novel training strategy is proposed. The key idea of the proposed training strategy is randomly regrouping the hidden units before each gradient descent step. Potentially, a mixing of infinite many iRBMs with different permutations of the hidden units can be achieved by this learning method, which has a similar effect of preventing the model from over-fitting as the dropout. The original iRBM is also modified to be capable of carrying out discriminative training. To evaluate the impact of our method on convergence speed of learning and the model's generalization ability, several experiments have been performed on the binarized MNIST and CalTech101 Silhouettes datasets. Experimental results indicate that the proposed training strategy can greatly accelerate learning and enhance generalization ability of iRBMs.

Well if you guessed it to be Alice you are correct. Perhaps your reasoning would be the content has words love, great and wonderful that are used by Alice. Now let's add a combination and probability in the data we have.Suppose Alice and Bob uses following words with probabilities as show below. Now, can you guess who is the sender for the content: "Wonderful Love." Now what do you think?

Recent work on imitation learning has generated policies that reproduce expert behavior from multi-modal data. However, past approaches have focused only on recreating a small number of distinct, expert maneuvers, or have relied on supervised learning techniques that produce unstable policies. This work extends InfoGAIL, an algorithm for multi-modal imitation learning, to reproduce behavior over an extended period of time. Our approach involves reformulating the typical imitation learning setting to include "burn-in demonstrations" upon which policies are conditioned at test time. We demonstrate that our approach outperforms standard InfoGAIL in maximizing the mutual information between predicted and unseen style labels in road scene simulations, and we show that our method leads to policies that imitate expert autonomous driving systems over long time horizons.

The automation of posterior inference in Bayesian data analysis has enabled experts and nonexperts alike to use more sophisticated models, engage in faster exploratory modeling and analysis, and ensure experimental reproducibility. However, standard automated posterior inference algorithms are not tractable at the scale of massive modern datasets, and modifications to make them so are typically model-specific, require expert tuning, and can break theoretical guarantees on inferential quality. Building on the Bayesian coresets framework, this work instead takes advantage of data redundancy to shrink the dataset itself as a preprocessing step, providing fully-automated, scalable Bayesian inference with theoretical guarantees. We begin with an intuitive reformulation of Bayesian coreset construction as sparse vector sum approximation, and demonstrate that its automation and performance-based shortcomings arise from the use of the supremum norm. To address these shortcomings we develop Hilbert coresets, i.e., Bayesian coresets constructed under a norm induced by an inner-product on the log-likelihood function space. We propose two Hilbert coreset construction algorithms---one based on importance sampling, and one based on the Frank-Wolfe algorithm---along with theoretical guarantees on approximation quality as a function of coreset size. Since the exact computation of the proposed inner-products is model-specific, we automate the construction with a random finite-dimensional projection of the log-likelihood functions. The resulting automated coreset construction algorithm is simple to implement, and experiments on a variety of models with real and synthetic datasets show that it provides high-quality posterior approximations and a significant reduction in the computational cost of inference.

In this paper, we study the Nystr{\"o}m type subsampling for large scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularization scheme based on Nystr{\"o}m type subsampling which is motivated from well-studied manifold regularization schemes. We develop a theoretical analysis of multi-penalty least-square regularization scheme under the general source condition in vector-valued function setting, therefore the results can also be applied to multi-task learning problems. We achieve the optimal minimax convergence rates of multi-penalty regularization using the concept of effective dimension for the appropriate subsampling size. We discuss an aggregation approach based on linear function strategy to combine various Nystr{\"o}m approximants. Finally, we demonstrate the performance of multi-penalty regularization based on Nystr{\"o}m type subsampling on Caltech-101 data set for multi-class image classification and NSL-KDD benchmark data set for intrusion detection problem.

Arkov decision processes (MDPs) have been widely used as a mathematical framework to solve stochastic sequential decision problems, such as autonomous driving [1], path planning [2], and quadrotor control [3]. In general, the goal of an MDP is to find the optimal policy function which maximizes the expected return. The expected return is a performance measure of a policy function and it is often defined as the expected sum of discounted rewards. An MDP is often used to formulate reinforcement learning (RL) [4], which aims to find the optimal policy without the explicit specification of stochasticity of an environment, and inverse reinforcement learning (IRL) [5], whose goal is to search the proper reward function that can explain the behavior of an expert who follows the underlying optimal policy. While the optimal solution of an MDP is a deterministic policy, it is not desirable to apply an MDP to the problems with multiple optimal actions. In perspective of RL, the knowledge of multiple optimal actions makes it possible to cope with unexpected situations. For example, suppose that an autonomous vehicle has multiple optimal routes to reach a given goal. If a traffic accident occurs at the currently selected optimal route, it is possible to avoid the accident by choosing another safe optimal route without additional computation of a new optimal route.

Here we discuss general applications of statistical models, whether they arise from data science, operations research, engineering, machine learning or statistics. We do not discuss specific algorithms such as decision trees, logistic regression, Bayesian modeling, Markov models, data reduction or feature selection. Instead, I discuss frameworks - each one using its own types of techniques and algorithms - to solve real life problems. Most of the entries below are found in Wikipedia, and I have used a few definitions or extracts from the relevant Wikipedia articles, in addition to personal contributions. Spatial dependency is the co-variation of properties within geographic space: characteristics at proximal locations appear to be correlated, either positively or negatively.

Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte Carlo techniques (M{\o}ller et al., 2006; Murray et al., 2006) for tackling this problem; these approaches being members of the more general class of pseudo-marginal, or exact-approximate, Monte Carlo algorithms (Andrieu and Roberts, 2009), which make use of unbiased estimates of intractable posteriors. Everitt et al. (2017) investigated the use of exact-approximate importance sampling (IS) and sequential Monte Carlo (SMC) in doubly intractable problems, but focussed only on SMC algorithms that used data-point tempering. This paper describes SMC samplers that may use alternative sequences of distributions, and describes ways in which likelihood estimates may be improved adaptively as the algorithm progresses, building on ideas from Moores et al. (2015). This approach is compared with a number of alternative algorithms for doubly intractable problems, including approximate Bayesian computation (ABC), which we show is closely related to the method of M{\o}ller et al. (2006).