To train an inference network jointly with a deep generative topic model, making it both scalable to big corpora and fast in out-of-sample prediction, we develop Weibull hybrid autoencoding inference (WHAI) for deep latent Dirichlet allocation, which infers posterior samples via a hybrid of stochastic-gradient MCMC and autoencoding variational Bayes. The generative network of WHAI has a hierarchy of gamma distributions, while the inference network of WHAI is a Weibull upward-downward variational autoencoder, which integrates a deterministic-upward deep neural network, and a stochastic-downward deep generative model based on a hierarchy of Weibull distributions. The Weibull distribution can be used to well approximate a gamma distribution with an analytic Kullback-Leibler divergence, and has a simple reparameterization via the uniform noise, which help efficiently compute the gradients of the evidence lower bound with respect to the parameters of the inference network. The effectiveness and efficiency of WHAI are illustrated with experiments on big corpora.

Many applications, including rank aggregation and crowd-labeling, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and columns. We consider the problem of estimating such a matrix based on noisy observations of a subset of its entries, and design and analyze polynomial-time algorithms that improve upon the state of the art. In particular, our results imply that any such $n \times n$ matrix can be estimated efficiently in the normalized Frobenius norm at rate $\widetilde{\mathcal O}(n^{-3/4})$, thus narrowing the gap between $\widetilde{\mathcal O}(n^{-1})$ and $\widetilde{\mathcal O}(n^{-1/2})$, which were hitherto the rates of the most statistically and computationally efficient methods, respectively.

Recent advances in the field of network embedding have shown the low-dimensional network representation is playing a critical role in network analysis. However, most of the existing principles of network embedding do not incorporate auxiliary information such as content and labels of nodes flexibly. In this paper, we take a matrix factorization perspective of network embedding, and incorporate structure, content and label information of the network simultaneously. For structure, we validate that the matrix we construct preserves high-order proximities of the network. Label information can be further integrated into the matrix via the process of random walk sampling to enhance the quality of embedding in an unsupervised manner, i.e., without leveraging downstream classifiers. In addition, we generalize the Skip-Gram Negative Sampling model to integrate the content of the network in a matrix factorization framework. As a consequence, network embedding can be learned in a unified framework integrating network structure and node content as well as label information simultaneously. We demonstrate the efficacy of the proposed model with the tasks of semi-supervised node classification and link prediction on a variety of real-world benchmark network datasets.

We propose SEARNN, a novel training algorithm for recurrent neural networks (RNNs) inspired by the "learning to search" (L2S) approach to structured prediction. RNNs have been widely successful in structured prediction applications such as machine translation or parsing, and are commonly trained using maximum likelihood estimation (MLE). Unfortunately, this training loss is not always an appropriate surrogate for the test error: by only maximizing the ground truth probability, it fails to exploit the wealth of information offered by structured losses. Further, it introduces discrepancies between training and predicting (such as exposure bias) that may hurt test performance. Instead, SEARNN leverages test-alike search space exploration to introduce global-local losses that are closer to the test error. We first demonstrate improved performance over MLE on two different tasks: OCR and spelling correction. Then, we propose a subsampling strategy to enable SEARNN to scale to large vocabulary sizes. This allows us to validate the benefits of our approach on a machine translation task.

In the medical community, there is a pressing need for personalized predictions of how a disruptive event, such as a treatment or disease, will impact particular bodily function levels. Of particular interest is the extent to which the function is initially perturbed by the event and the ensuing pattern of recovery. In many contexts, such as mental acuity following a stroke or sexual function following prostatectomy, the post-event trajectory generally exhibits what we call a recovery curve shape, characterized by an initial instantaneous drop followed by a monotonic rise towards an asymptotic level not exceeding the original function level. Here, we propose a Bayesian model that can be used to predict a patient's expected recovery curve, given information about the patient that is available before the event. This paper presents a decision aid for patients considering a medical treatment who want to know what adverse side effect the treatment would have on a particular bodily function. In particular, our model will be used to display to the patient a distribution over post-treatment function trajectories, conveying the uncertainty in predictions that should be considered in decision-making.

The need for parameter estimation with massive data has reinvigorated interest in iterative estimation procedures. Stochastic approximations, such as stochastic gradient descent, are at the forefront of this recent development because they yield simple, generic, and extremely fast iterative estimation procedures. Such stochastic approximations, however, are often numerically unstable. As a consequence, current practice has turned to proximal operators, which can induce stable parameter updates within iterations. While the majority of classical iterative estimation procedures are subsumed by the framework of Robbins and Monro (1951), there is no such generalization for stochastic approximations with proximal updates. In this paper, we conceptualize a general stochastic approximation method with proximal updates. This method can be applied even in situations where the analytical form of the objective is not known, and so it generalizes many stochastic gradient procedures with proximal operators currently in use. Our theoretical analysis indicates that the proposed method has important stability benefits over the classical stochastic approximation method. Exact instantiations of the proposed method are challenging, but we show that approximate instantiations lead to procedures that are easy to implement, and still dominate classical procedures by achieving numerical stability without tradeoffs. This last advantage is akin to that seen in deterministic proximal optimization, where the framework is typically impossible to instantiate exactly, but where approximate instantiations lead to new optimization procedures that dominate classical ones.

The logarithm is an interesting character. Let us only understand its personality applicable for regression models. The fundamental property of a logarithm is its base. The typical base of the logarithm is 2, 10 or e. There is another common base for logarithms.

Business Intelligence is a technology that is used to gather, store, access and analyzes data to help business users in making better decisions, on the other hand, Artificial Intelligence is a way to make a computer, a computer-controlled robot, or a software that think intelligently like humans.Artificial Intelligence is based on the study that how human thinks, learn, decide and work in order to resolve an issue and then using the outcome of this study as a basis of developing intelligent software and systems. It starts from root node and explores neighbor nodes first and moves to the next level neighbor nodes.It provides the shortest path to the solution and can be implemented using FIFO This algorithm is implemented using LIFO(Last in first out)data structure.It creates nodes same as breadth-first search but it differs in only order.In each iteration, it stores the nodes from root to leaf and also it cannot check duplicate nodes. It makes predictions by using Bayes algorithm, which derives probability prediction from the underlying evidence, as observed in data. In this algorithm, sorting is done in increasing cost of the path to a node.It always expands the least cost node.This search is identical to the Breadth-first search if each transition has the same cost.It explores the path in the increasing order of cost. It implements logistic regression for classification of binary targets and linear regression for continuous targets.It supports confidence bounds for prediction probabilities and also supports confidence bounds for prediction. It performs the depth-first search at level-1 and starts over, then executes a complete depth-first search to level 2, and continues till it gets the solution.

Linear regression is used for finding linear relationship between target and one or more predictors. There are two types of linear regression- Simple and Multiple. Simple linear regression is useful for finding relationship between two continuous variables. One is predictor or independent variable and other is response or dependent variable. It looks for statistical relationship but not deterministic relationship.

MCMC (Markov chain Monte Carlo) is a family of methods that are applied in computational physics and chemistry and also widely used in bayesian machine learning. It is used to simulate physical systems with Gibbs canonical distribution: $$ p(\vx) \propto \exp\left( - \frac{U(\vx)}{T} \right) $$ Probability $ p(\vx) $ of a system to be in the state $ \vx $ depends on the energy of the state $U(\vx)$ and temperature $ T $ . This distribution describes positions and velocities of particles in the gas, for instance. In bayesian machine learning, it defines distribution of model parameters (such as weights of a neural network). For example, consider a multivariate normal distribution: $$ p(\vx) \propto \exp\left( - \dfrac{1}{2} (\vx - \mu) T \Sigma {-1} (\vx - \mu) \right) $$ which corresponds to the following potential energy: $$ U(\vx) \dfrac{1}{2} (\vx - \mu) T \Sigma {-1} (\vx - \mu), \qquad T 1. $$ Any distribution can be rewritten as Gibbs canonical distribution, but for many problems such energy-based distributions appear very naturally.