In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The presence of sparse noise is handled using appropriate use of $\ell_1$-norm along-with use of $\ell_2$-norm in a convex cost function. For optimization of the cost function, we propose an iteratively reweighted least-squares (IRLS) approach that is suitable for kernel substitution or kernel trick due to availability of a closed form solution. Simulations using real-world temperature data show efficacy of our proposed method, mainly for limited-size training datasets.

Analysis of the Bitcoin Blockchain [26] is an area of intense activity [20, 1], and one which has witnessed an explosion of interest as the value of the Bitcoin cryptocurrency hasskyrocketed. Research areas include explorations of address clustering techniques toidentify logical agents [11, 21, 11, 7], de-anonymization using side-channel attacks [8, 13]. An understanding of the properties of Bitcoin transactions is paramount to the legitimation ofthe cryptocurrency economy; it constitutes a building block to the conception of effective and adequate regulations [9], and to the design of novel and integrated services benefiting society as a whole. As of 2018, with more than 500 million address nodes, the Bitcoin graph is comparable insize to a large social network. Yet while probabilistic models of social networks have received considerable attention, from community detection [19] to diffusion models andinfluence maximization [34], to probabilistic graph modeling [17], probabilistic models of the Bitcoin Blockchain network have not. 1 Bitcoin transactions are tantamount to a partially observed social network, within which participants can have multiple seemingly independent aliases.

This research aims to identify how Bitcoin-related news publications and online discourse are expressed in Bitcoin exchange movements of price and volume. Being inherently digital, all Bitcoin-related fundamental data (from exchanges, as well as transactional data directly from the blockchain) is available online, something that is not true for traditional businesses or currencies traded on exchanges. This makes Bitcoin an interesting subject for such research, as it enables the mapping of sentiment to fundamental events that might otherwise be inaccessible. Furthermore, Bitcoin discussion largely takes place on online forums and chat channels. In stock trading, the value of sentiment data in trading decisions has been demonstrated numerous times [1] [2] [3], and this research aims to determine whether there is value in such data for Bitcoin trading models. To achieve this, data over the year 2015 has been collected from Bitcointalk.org, (the biggest Bitcoin forum in post volume), established news sources such as Bloomberg and the Wall Street Journal, the complete /r/btc and /r/Bitcoin subreddits, and the bitcoin-otc and bitcoin-dev IRC channels. By analyzing this data on sentiment and volume, we find weak to moderate correlations between forum, news, and Reddit sentiment and movements in price and volume from 1 to 5 days after the sentiment was expressed. A Granger causality test confirms the predictive causality of the sentiment on the daily percentage price and volume movements, and at the same time underscores the predictive causality of market movements on sentiment expressions in online communities

In this paper, we consider the problem of selecting representatives from a data set for arbitrary supervised/unsupervised learning tasks. We identify a subset $S$ of a data set $A$ such that 1) the size of $S$ is much smaller than $A$ and 2) $S$ efficiently describes the entire data set, in a way formalized via auto-regression. The set $S$, also known as the exemplars of the data set $A$, is constructed by solving a convex auto-regressive version of dictionary learning where the dictionary and measurements are given by the data matrix. We show that in order to generate $|S| = k$ exemplars, our algorithm, Frank-Wolfe Sparse Representation (FWSR), only requires $\approx k$ iterations with a per-iteration cost that is quadratic in the size of $A$, an order of magnitude faster than state of the art methods. We test our algorithm against current methods on 4 different data sets and are able to outperform other exemplar finding methods in almost all scenarios. We also test our algorithm qualitatively by selecting exemplars from a corpus of Donald Trump and Hillary Clinton's twitter posts.

The ability to perform offline A/B-testing and off-policy learning using logged contextual bandit feedback is highly desirable in a broad range of applications, including recommender systems, search engines, ad placement, and personalized health care. Both offline A/B-testing and off-policy learning require a counterfactual estimator that evaluates how some new policy would have performed, if it had been used instead of the logging policy. This paper proposes a new counterfactual estimator - called Continuous Adaptive Blending (CAB) - for this policy evaluation problem that combines regression and weighting approaches for an effective bias/variance trade-off. It can be substantially less biased than clipped Inverse Propensity Score weighting and the Direct Method, and it can have less variance compared with Doubly Robust and IPS estimators. Experimental results show that CAB provides excellent and reliable estimation accuracy compared to other blended estimators, and - unlike the SWITCH estimator - is sub-differentiable such that it can be used for learning.

Recent advances in deep learning have achieved impressive gains in classification accuracy on a variety of types of data, including images and text. Despite these gains, however, concerns have been raised about the interpretability of these models, as well as issues related to calibration and robustness. In this paper we propose a simple way to modify any conventional deep architecture to automatically provide more transparent explanations for classification decisions, as well as an intuitive notion of the credibility of each prediction. Specifically, we draw on ideas from nonparametric kernel regression, and propose to predict labels based on a weighted sum of training instances, where the weights are determined by distance in a learned instance-embedding space. Working within the framework of conformal methods, we propose a new measure of nonconformity suggested by our model, and experimentally validate the accompanying theoretical expectations, demonstrating improved transparency, controlled error rates, and robustness to out-of-domain data, without compromising on accuracy or calibration.

Adaptive moment methods have been remarkably successful in deep learning optimization, particularly in the presence of noisy and/or sparse gradients. We further the advantages of adaptive moment techniques by proposing a family of double adaptive stochastic gradient methods~\textsc{DASGrad}. They leverage the complementary ideas of the adaptive moment algorithms widely used by deep learning community, and recent advances in adaptive probabilistic algorithms.We analyze the theoretical convergence improvements of our approach in a stochastic convex optimization setting, and provide empirical validation of our findings with convex and non convex objectives. We observe that the benefits of~\textsc{DASGrad} increase with the model complexity and variability of the gradients, and we explore the resulting utility in extensions of distribution-matching multitask learning.

In this paper, we propose a novel linear discriminant analysis criterion via the Bhattacharyya error bound estimation based on a novel L1-norm (L1BLDA) and L2-norm (L2BLDA). Both L1BLDA and L2BLDA maximize the between-class scatters which are measured by the weighted pairwise distances of class means and meanwhile minimize the within-class scatters under the L1-norm and L2-norm, respectively. The proposed models can avoid the small sample size (SSS) problem and have no rank limit that may encounter in LDA. It is worth mentioning that, the employment of L1-norm gives a robust performance of L1BLDA, and L1BLDA is solved through an effective non-greedy alternating direction method of multipliers (ADMM), where all the projection vectors can be obtained once for all. In addition, the weighting constants of L1BLDA and L2BLDA between the between-class and within-class terms are determined by the involved data set, which makes our L1BLDA and L2BLDA adaptive. The experimental results on both benchmark data sets as well as the handwritten digit databases demonstrate the effectiveness of the proposed methods.

In multi-view learning, features are organized into multiple sets called views. Multi-view stacking (MVS) is an ensemble learning framework which learns a prediction function from each view separately, and then learns a meta-function which optimally combines the view-specific predictions. In case studies, MVS has been shown to increase prediction accuracy. However, the framework can also be used for selecting a subset of important views. We propose a method for selecting views based on MVS, which we call stacked penalized logistic regression (StaPLR). Compared to existing view-selection methods like the group lasso, StaPLR can make use of faster optimization algorithms and is easily parallelized. We show that nonnegativity constraints on the parameters of the function which combines the views are important for preventing unimportant views from entering the model. We investigate the view selection and classification performance of StaPLR and the group lasso through simulations, and consider two real data examples. We observe that StaPLR is less likely to select irrelevant views, leading to models that are sparser at the view level, but which have comparable or increased predictive performance.

The exponential family is one of the most important classes of distributions in statistics and machine learning. The exponential family possesses a number of useful properties (Brown, 1986)and includes many commonly used distributions with finite-dimensional natural parameters, such as the Gaussian, Poisson and multinomial distributions, to name a few. It is natural to consider generalizing the richness and flexibility of the exponential family to an infinite-dimensional parameterization via reproducing kernel Hilbert spaces (RKHS) (Canu and Smola, 2006) Maximum log-likelihood estimation (MLE) has already been well-studied in the case of finite-dimensional exponential families, where desirable statistical properties such as asymptotic unbiasedness, consistency and asymptotic normality have been established. However, it is difficult to extend MLE to the infinitedimensional case. Beyond the intractability of evaluating the partition function for a general exponential family, the necessary conditions for maximizing log-likelihood might not be feasible; that is, there may be no solution to the KKT conditions in the infinite-dimensional case (Pistone and Rogantin, 1999; Fukumizu, 2009). To address this problem, Barron and Sheu (1991); Gu and Qiu (1993); Fukumizu (2009) considered several ways to regularize the function space by constructing (a series of) finite-dimensional spaces that approximate the original RKHS, yielding a tractable estimator in the restricted finite-dimensional space. However, as Sriperumbudur et al. (2017) note, even with the finite-dimension approximation, these algorithms are still expensive as every update requires Monte-Carlo sampling from a current model to compute the partition function.