We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal model. We show that the variables in the marginal model are non-Gaussian distributed and their expected relations are nonlinear. We use expectation-maximization to break the inference of the nonlinear model into a sequence of TGGM inference problems, each of which is efficiently solved by using the properties and numerical methods of multivariate Gaussian distributions. We use the TGGM to design models for nonlinear regression and classification, with the performances of these models demonstrated on extensive benchmark datasets and compared to state-of-the-art competing results.

Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling abilities, due to the Gaussian assumption. In this paper, we introduce a novel variant of GGMs, which relaxes the Gaussian restriction and yet admits efficient inference. Specifically, we impose a bipartite structure on the GGM and govern the hidden variables by truncated normal distributions. The nonlinearity of the model is revealed by its connection to rectified linear unit (ReLU) neural networks. Meanwhile, thanks to the bipartite structure and appealing properties of truncated normals, we are able to train the models efficiently using contrastive divergence. We consider three output constructs, accounting for real-valued, binary and count data. We further extend the model to deep constructions and show that deep models can be used for unsupervised pre-training of rectifier neural networks. Extensive experimental results are provided to validate the proposed models and demonstrate their superiority over competing models.

Abstract--A number of important applied problems in engineering, finance and medicine can be formulated as a problem of anomaly detection based on a one-class classification. A classical approach to this problem is to describe a normal state using a one-class support vector machine. Then to detect anomalies we quantify a distance from a new observation to the constructed description of the normal class. In this paper we present a new approach to one-class classification. We formulate a new problem statement and a corresponding algorithm that allow taking into account privileged information during the training phase. We evaluate performance of the proposed approach using synthetic datasets, as well as the publicly available Microsoft Malware Classification Challenge dataset. Anomaly detection refers to the problem of finding patterns in data that do not conform to an expected behaviour.

Empirical Risk Minimization (ERM) is a standard technique in machine learning, where a model is selected by minimizing a loss function over constraint set. When the training dataset consists of private information, it is natural to use a differentially private ERM algorithm, and this problem has been the subject of a long line of work started with Chaudhuri and Monteleoni 2008. A private ERM algorithm outputs an approximate minimizer of the loss function and its error can be measured as the difference from the optimal value of the loss function. When the constraint set is arbitrary, the required error bounds are fairly well understood \cite{BassilyST14}. In this work, we show that the geometric properties of the constraint set can be used to derive significantly better results. Specifically, we show that a differentially private version of Mirror Descent leads to error bounds of the form $\tilde{O}(G_{\mathcal{C}}/n)$ for a lipschitz loss function, improving on the $\tilde{O}(\sqrt{p}/n)$ bounds in Bassily, Smith and Thakurta 2014. Here $p$ is the dimensionality of the problem, $n$ is the number of data points in the training set, and $G_{\mathcal{C}}$ denotes the Gaussian width of the constraint set that we optimize over. We show similar improvements for strongly convex functions, and for smooth functions. In addition, we show that when the loss function is Lipschitz with respect to the $\ell_1$ norm and $\mathcal{C}$ is $\ell_1$-bounded, a differentially private version of the Frank-Wolfe algorithm gives error bounds of the form $\tilde{O}(n^{-2/3})$. This captures the important and common case of sparse linear regression (LASSO), when the data $x_i$ satisfies $|x_i|_{\infty} \leq 1$ and we optimize over the $\ell_1$ ball. We show new lower bounds for this setting, that together with known bounds, imply that all our upper bounds are tight.

Contributes Intel Apache Spark* Spark Users *Other names and brands may be claimed as the property of others 3. Sparse data is almost everywhere • Data Source: – Movie ratings – Purchase history • Feature engineering: – NLP: CountVectorizer, HashingTF – Categorical: OneHotEncoder – Image, video 0 1 2 3 4 5 6 7 8 9 10 0 2 4 6 8 10 Customers products Purchase History 4. Sparse data support in MLlib new DenseVector( values Array(1.0, Sparse data support in MLlib • Supporting Sparse data since v1.0 – Load / Save, Sparse Vector, LIBSVM – Supporting sparse vector is one of the primary review focus. KMeans • Pick initial cluster centers – Random – KMeans • Iterative training – Points clustering, find nearest center for each point – Re-compute center in each cluster (avg.) MLlib iteration 2. Compute a sum table for each partition of data val sum new Array[Vector](k) for (each point in the partition) { val bestCenter traverse() sum(bestCenter) point } Training dataset Executor 1 Executor 2 Executor 3 Sums: 16G Centers: 16G *Other names and brands may be claimed as the property of others 14. Analysis: Data • Are the cluster centers dense?

To produce a regression analysis of inference that can be justified or trustworthy in the sense that helpful. The term in the statistical methods that generate a linear the best estimator is not bias (best linear unbiased estimator) abbreviated BLUE. Then there are some other things that are also important to note, in which the data to be processed, must meet certain requirements. All terms or phases of the classical assumptions that must be met, in order to build a regression model that could be accounted for. Thus, the need to test that assumption is intended to meet some of the elements of the accuracy of the parameter estimator is not biased to reflect the efficient level of analysis results are consistent so that the regression equation can be trusted.

Udacity 291 views Show Developer Workflow - Duration: 2:09.

Privacy policies are commonly used to inform users about the data collection and use practices of websites, mobile apps, and other products and services. However, the average Internet user struggles to understand the contents of these documents and generally does not read them. Natural language and machine learning techniques offer the promise of automatically extracting relevant statements from privacy policies to help generate succinct summaries, but current techniques require large amounts of annotated data. The highest quality annotations require law experts, but their efforts do not scale efficiently. In this paper, we present results on bridging the gap between privacy practice categories defined by law experts with topics learned from Non-negative Matrix Factorization (NMF). To do this, we investigate the intersections between vocabulary sets identified as most significant for each category, using a logistic regression model, and vocabulary sets identified by topic modeling. The intersections exhibit strong matches between some categories and topics, although other categories have weaker affinities with topics. Our results show a path forward for applying unsupervised methods to the determination of data practice categories in privacy policy text.

While social networks can provide an ideal platform for up-to-date information from individuals across the world, it has also proved to be a place where rumours fester and accidental or deliberate misinformation often emerges. In this article, we aim to support the task of making sense from social media data, and specifically, seek to build an autonomous message-classifier that filters relevant and trustworthy information from Twitter. For our work, we collected about 100 million public tweets, including users' past tweets, from which we identified 72 rumours (41 true, 31 false). We considered over 80 trustworthiness measures including the authors' profile and past behaviour, the social network connections (graphs), and the content of tweets themselves. We ran modern machine-learning classifiers over those measures to produce trustworthiness scores at various time windows from the outbreak of the rumour. Such time-windows were key as they allowed useful insight into the progression of the rumours. From our findings, we identified that our model was significantly more accurate than similar studies in the literature. We also identified critical attributes of the data that give rise to the trustworthiness scores assigned. Finally we developed a software demonstration that provides a visual user interface to allow the user to examine the analysis.

Over the past two years I've noticed a steady stream of articles in the mainstream press and business journals centred on the themes of a) the dangers of machine learning 1 2 or b) the limitations of machine learning 3 4. Many of these articles refer to incidents where machine learning initiatives have echoed and exasperated our own biases, prejudices and (frankly racist) behaviours 5. Others have focused on their limitations with providing the sorts of'informed, idiosyncratic' recommendations that humans find effortless. However, for those of us that work in the field of predictive analytics where many of the algorithms at the heart of these stories are routinely used, 'machine learning' is nothing new. In fact, many of us are pretty bemused by the fact that the media has leapt on the phrase'machine learning' to stand for everything from multivariate statistics, association modelling and rule induction to operational research, cognitive computing and artificial intelligence. Rather like the word'algorithm' it's being used to cover pretty much any situation where software generates predictions in the form of risk scores, recommendations, estimates or classifications.