In this paper, we develop a non-parametric Bayesian estimation of Hawkes process kernel functions. Our method is based on the cluster representation of Hawkes processes. We sample random branching structures, and thus split the Hawkes process into clusters of Poisson processes, where the intensity function of each of these processes is the nonparametric triggering kernel of the Hawkes process. We derive both a block Gibbs sampler and a maximum a posteriori estimator based on stochastic expectation maximization. On synthetic data, we show our method to be flexible and scalable, and on two largescale Twitter diffusion datasets, we show our method to outperform the parametric Hawkes model. We observe that the learned non-parametric kernel reflects the longevity of different content types. Code has been made publicly available.

We investigate deep Bayesian neural networks with Gaussian priors on the weights and ReLU-like nonlinearities, shedding light on novel sparsity-inducing mechanisms at the level of the units of the network, both pre- and post-nonlinearities. The main thrust of the paper is to establish that the units prior distribution becomes increasingly heavy-tailed with depth. We show that first layer units are Gaussian, second layer units are sub-Exponential, and we introduce sub-Weibull distributions to characterize the deeper layers units. Bayesian neural networks with Gaussian priors are well known to induce the weight decay penalty on the weights. In contrast, our result indicates a more elaborate regularisation scheme at the level of the units, ranging from convex penalties for the first two layers - weight decay for the first and Lasso for the second - to non convex penalties for deeper layers. Thus, despite weight decay does not allow for the weights to be set exactly to zero, sparse solutions tend to be selected for the units from the second layer onward. This result provides new theoretical insight on deep Bayesian neural networks, underpinning their natural shrinkage properties and practical potential.

We propose PANDA, an AdaPtive Noise Augmentation technique to regularize estimating and constructing undirected graphical models (UGMs). PANDA iteratively solves MLEs given noise augmented data in the regression-based framework until convergence to achieve the designed regularization effects. The augmented noises can be designed to achieve various regularization effects on graph estimation, including the bridge, elastic net, adaptive lasso, and SCAD penalization; it can also offer group lasso and fused ridge when some nodes belong to the same group. We establish theoretically that the noise-augmented loss functions and its minimizer converge almost surely to the expected penalized loss function and its minimizer, respectively. We derive the asymptotic distributions for the regularized regression coefficients through PANDA in GLMs, based on which, the inferences for the parameters can be obtained simultaneously with variable selection. Our empirical results suggest the inferences achieve nominal or near-nominal coverage and are far more efficient compared to some existing post-selection procedures. On the algorithm level, PANDA can be easily programmed in any standard software without resorting to complicated optimization techniques. We show the non-inferior performance of PANDA in constructing graphs of different types in simulation studies and also apply PANDA to the autism spectrum disorder data to construct a mixed-node graph.

The Viterbi process is the limiting maximum a-posteriori estimate of the unobserved path in a hidden Markov model as the length of the time horizon grows. The existence of such a process suggests that approximate estimation using optimization algorithms which process data segments in parallel may be accurate. For models on state-space $\mathbb{R}^{d}$ satisfying a new "decay-convexity" condition, we approach the existence of the Viterbi process through fixed points of ordinary differential equations in a certain infinite dimensional Hilbert space. Quantitative bounds on the distance to the Viterbi process show that approximate estimation via parallelization can indeed be accurate and scaleable to high-dimensional problems because the rate of convergence to the Viterbi process does not necessarily depend on $d$.

Learning robot objective functions from human input has become increasingly important, but state-of-the-art techniques assume that the human's desired objective lies within the robot's hypothesis space. When this is not true, even methods that keep track of uncertainty over the objective fail because they reason about which hypothesis might be correct, and not whether any of the hypotheses are correct. We focus specifically on learning from physical human corrections during the robot's task execution, where not having a rich enough hypothesis space leads to the robot updating its objective in ways that the person did not actually intend. We observe that such corrections appear irrelevant to the robot, because they are not the best way of achieving any of the candidate objectives. Instead of naively trusting and learning from every human interaction, we propose robots learn conservatively by reasoning in real time about how relevant the human's correction is for the robot's hypothesis space. We test our inference method in an experiment with human interaction data, and demonstrate that this alleviates unintended learning in an in-person user study with a 7DoF robot manipulator.

Abstract-- Feature Selection (FS) plays an important role in learning and classification tasks. The object of FS is to select the relevant and non-redundant features. Considering the huge amount number of features in real-world applications, FS methods using batch learning technique can't resolve big data problem especially when data arrive sequentially. In this paper, we propose an online feature selection system which resolves this problem. More specifically, we treat the problem of online supervised feature selection for binary classification as a decision-making problem. A philosophical vision to this problem leads to a hybridization between two important domains: feature selection using online learning technique (OFS) and automated negotiation (AN). The proposed OFS system called MOANOFS (Multi-Objective Automated Negotiation based Online Feature Selection) uses two levels of decision. In the first level, from n learners (or OFS methods), we decide which are the k trustful ones (with high confidence or trust value). These elected k learners will participate in the second level. In this level, we integrate our proposed Multilateral Automated Negotiation based OFS (MANOFS) method to decide finally which is the best solution or which are relevant features. We show that MOANOFS system is applicable to different domains successfully and achieves high accuracy with several real-world applications. Index Terms-- Feature selection, online learning, multi-objective automated negotiation, trust, classification, big data. URING the last three decades, Feature Selection (FS) has been extensively studied in Data Mining [1], [2], Pattern Classification [3], [4] and Machine Learning [5], [6]. FS is defined as the process of selecting a subset of relevant features and removing the redundant ones from a dataset for building effective prediction models. In recent years, an enormous increase in data (news, medical imaging) has been observed which allows an increase in redundant information. Even worse, the redundancy of irrelevant data has a negative impact on the performance of classification methods associated. With the rapid development of the Internet, current tremendous amounts of data up to millions or billions, can be collected for training machine learning models.

Compared to the classic latent factor models [14], latent feature models have two main benefits: (1) interpretablity: the binary codes directly reveal whether certain features exist in the data, thus provide more interpretable latent profiles [25]; (2) scalability: compared with real-valued codes, binary codes require fewer bits to store, thereby cutting down the memory footprint, making it easier to deploy into memory constrained environments such as mobile devices. Tensor latent feature models generalize traditional matrix latent feature models to represent high-order correlation structures in the data. For example, in spatiotemporal recommender systems, the observations are user activities over different locations and time. We want to learn the latent features and codes that correspond to user, space and time simultaneously without assuming conditional independence of these three dimensions. In this case, we can first represent such data as a high-order tensor and assign binary codes encoding presence or absence of rows for individual modes of the tensor. These codes can then help us answer the "when" and "where" questions regarding the learned user preferences. Besides the non-convex formulation of the maximum likelihood estimation (MLE) objective, learning latent feature models is further complicated by the combinatorial nature of the codes.

Naive Bayes is the most simple algorithm that you can apply to your data. As the name suggests, here this algorithm makes an assumption as all the variables in the dataset is "Naive" i.e not correlated to each other. Naive Bayes is a very popular classification algorithm that is mostly used to get the base accuracy of the dataset. Let's assume that you are walking on the playground. Now you see some red object in front of you.

Still confused about deep learning, how it works, what is its shortcomings, and what is its origins? Paraphrasing Zoubin: Deep learning is neural networks rebranded. Compute power enables us to run many layers of weighted computational neurons, hence the phrase "deep". They are data hungry, computationally intensive, uninterpretable black boxes that can be easily fooled. But ... They can do amazing things and using them is becoming easier.

Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes (VB) is theoretically grounded, generally applicable, and computationally efficient. With wide recognition of potential advantages, why is it that variational Bayes has seen very limited practical use for BNNs in real applications? We argue that variational inference in neural networks is fragile: successful implementations require careful initialization and tuning of prior variances, as well as controlling the variance of Monte Carlo gradient estimates. We fix VB and turn it into a robust inference tool for Bayesian neural networks. We achieve this with two innovations: first, we introduce a novel deterministic method to approximate moments in neural networks, eliminating gradient variance; second, we introduce a hierarchical prior for parameters and a novel empirical Bayes procedure for automatically selecting prior variances. Combining these two innovations, the resulting method is highly efficient and robust. On the application of heteroscedastic regression we demonstrate strong predictive performance over alternative approaches.