We propose sparse estimation methods for the generalized linear models, which run Least Angle Regression (LARS) and Least Absolute Shrinkage and Selection Operator (LASSO) in the tangent space of the manifold of the statistical model. Our approach is to roughly approximate the statistical model and to subsequently use exact calculations. LARS was proposed as an efficient algorithm for parameter estimation and variable selection for the normal linear model. The LARS algorithm is described in terms of Euclidean geometry with regarding correlation as metric of the space. Since the LARS algorithm only works in Euclidean space, we transform a manifold of the statistical model into the tangent space at the origin. In the generalized linear regression, this transformation allows us to run the original LARS algorithm for the generalized linear models. The proposed methods are efficient and perform well. Real-data analysis shows that the proposed methods output similar results as that of the $l_1$-penalized maximum likelihood estimation for the generalized linear models. Numerical experiments show that our methods work well and they can be better than the $l_1$-penalization for the generalized linear models in generalization, parameter estimation, and model selection.

A large number and diversity of techniques have been offered in the literature in recent years for solving multi-label classification tasks, including classifier chains where predictions are cascaded to other models as additional features. The idea of extending this chaining methodology to multi-output regression has already been suggested and trialed: regressor chains. However, this has so-far been limited to greedy inference and has provided relatively poor results compared to individual models, and of limited applicability. In this paper we identify and discuss the main limitations, including an analysis of different base models, loss functions, explainability, and other desiderata of real-world applications. To overcome the identified limitations we study and develop methods for regressor chains. In particular we present a sequential Monte Carlo scheme in the framework of a probabilistic regressor chain, and we show it can be effective, flexible and useful in several types of data. We place regressor chains in context in general terms of multi-output learning with continuous outputs, and in doing this shed additional light on classifier chains.

We develop tools for utilizing correspondence experiments to detect illegal discrimination by individual employers. Employers violate US employment law if their propensity to contact applicants depends on protected characteristics such as race or sex. We establish identification of higher moments of the causal effects of protected characteristics on callback rates as a function of the number of fictitious applications sent to each job ad. These moments are used to bound the fraction of jobs that illegally discriminate. Applying our results to three experimental datasets, we find evidence of significant employer heterogeneity in discriminatory behavior, with the standard deviation of gaps in job-specific callback probabilities across protected groups averaging roughly twice the mean gap. In a recent experiment manipulating racially distinctive names, we estimate that at least 85% of jobs that contact both of two white applications and neither of two black applications are engaged in illegal discrimination. To assess the tradeoff between type I and II errors presented by these patterns, we consider the performance of a series of decision rules for investigating suspicious callback behavior under a simple two-type model that rationalizes the experimental data. Though, in our preferred specification, only 17% of employers are estimated to discriminate on the basis of race, we find that an experiment sending 10 applications to each job would enable accurate detection of 7-10% of discriminators while falsely accusing fewer than 0.2% of non-discriminators. A minimax decision rule acknowledging partial identification of the joint distribution of callback rates yields higher error rates but more investigations than our baseline two-type model. Our results suggest illegal labor market discrimination can be reliably monitored with relatively small modifications to existing audit designs.

The evolution and development of events have their own basic principles, which make events happen sequentially. Therefore, the discovery of such evolutionary patterns among events are of great value for event prediction, decision-making and scenario design of dialog systems. However, conventional knowledge graph mainly focuses on the entities and their relations, which neglects the real world events. In this paper, we present a novel type of knowledge base - Event Logic Graph (ELG), which can reveal evolutionary patterns and development logics of real world events. Specifically, ELG is a directed cyclic graph, whose nodes are events, and edges stand for the sequential, causal or hypernym-hyponym (is-a) relations between events. We constructed two domain ELG: financial domain ELG, which consists of more than 1.5 million of event nodes and more than 1.8 million of directed edges, and travel domain ELG, which consists of about 30 thousand of event nodes and more than 234 thousand of directed edges. Experimental results show that ELG is effective for the task of script event prediction.

This paper introduces a la carte embed-ding, a simple and general alternative to the usual word2vec-based approaches for building such representations that is based upon recent theoretical results for GloVe-like embeddings. Our method relies mainly on a linear transfor-mation that is efficiently learnable using pretrained word vectors and linear regression. This transform is applicable on the fly in the future when a new text feature or rare word is encountered, even if only a single usage example is available. We introduce a new dataset showing how the a la carte method requires fewer examples of words in con-text to learn high-quality embeddings and we obtain state-of-the-art results on a nonce task and some unsupervised document classification tasks.

Instead of only comparing XGBoost and Random Forest in this post we will try to explain how to use those two very popular approaches with Bayesian Optimisation and that are those models main pros and cons. XGBoost (XGB) and Random Forest (RF) both are ensemble learning methods and predict (classification or regression) by combining the outputs from individual decision trees (we assume tree-based XGB or RF). XGBoost build decision tree one each time. Each new tree corrects errors which were made by previously trained decision tree. At Addepto we use XGBoost models to solve anomaly detection problems e.g. in supervised learning approach.

Rectified Linear Units (ReLU) have become the main model for the neural units in current deep learning systems. This choice has been originally suggested as a way to compensate for the so called vanishing gradient problem which can undercut stochastic gradient descent (SGD) learning in networks composed of multiple layers. Here we provide analytical results on the effects of ReLUs on the capacity and on the geometrical landscape of the solution space in two-layer neural networks with either binary or real-valued weights. We study the problem of storing an extensive number of random patterns and find that, quite unexpectedly, the capacity of the network remains finite as the number of neurons in the hidden layer increases, at odds with the case of threshold units in which the capacity diverges. Possibly more important, a large deviation approach allows us to find that the geometrical landscape of the solution space has a peculiar structure: while the majority of solutions are close in distance but still isolated, there exist rare regions of solutions which are much more dense than the similar ones in the case of threshold units. These solutions are robust to perturbations of the weights and can tolerate large perturbations of the inputs. The analytical results are corroborated by numerical findings.

Often domain adaptation is performed using a discriminator (domain One such adversarial domain-invariant feature learning method classifier) to learn domain-invariant feature representations is the domain-adversarial neural network (DANN) [14, 15], which so that a classifier trained on labeled source data will generalize is a typical baseline for other variants. This method consists of a feature well to unlabeled target data. A line of research stemming from extractor network followed by two additional networks: a task semi-supervised learning uses pseudo labeling to directly generate classifier and a domain classifier (Figure 1). The network is updated "pseudo labels" for the unlabeled target data and trains a classifier by two competing objectives: (1) the feature extractor followed by on the now-labeled target data, where the samples are selected the task classifier learns to correctly classify the labeled source data or weighted based on some measure of confidence. In this paper, while the domain classifier learns to correctly predict whether the we propose multi-purposing the discriminator to not only aid in features originated from source or target data, and (2) the feature producing domain-invariant representations but also to provide extractor learns to make the domain classifier predict the domain pseudo labeling confidence.

This paper investigates different vector step-size adaptation approaches for non-stationary online, continual prediction problems. Vanilla stochastic gradient descent can be considerably improved by scaling the update with a vector of appropriately chosen step-sizes. Many methods, including AdaGrad, RMSProp, and AMSGrad, keep statistics about the learning process to approximate a second order update---a vector approximation of the inverse Hessian. Another family of approaches use meta-gradient descent to adapt the step-size parameters to minimize prediction error. These meta-descent strategies are promising for non-stationary problems, but have not been as extensively explored as quasi-second order methods. We first derive a general, incremental meta-descent algorithm, called AdaGain, designed to be applicable to a much broader range of algorithms, including those with semi-gradient updates or even those with accelerations, such as RMSProp. We provide an empirical comparison of methods from both families. We conclude that methods from both families can perform well, but in non-stationary prediction problems the meta-descent methods exhibit advantages. Our method is particularly robust across several prediction problems, and is competitive with the state-of-the-art method on a large-scale, time-series prediction problem on real data from a mobile robot.

Canonical Correlation Analysis (CCA) is widely used for multimodal data analysis and, more recently, for discriminative tasks such as multi-view learning; however, it makes no use of class labels. Recent CCA methods have started to address this weakness but are limited in that they do not simultaneously optimize the CCA projection for discrimination and the CCA projection itself, or they are linear only. We address these deficiencies by simultaneously optimizing a CCA-based and a task objective in an end-to-end manner. Together, these two objectives learn a non-linear CCA projection to a shared latent space that is highly correlated and discriminative. Our method shows a significant improvement over previous state-of-the-art (including deep supervised approaches) for cross-view classification, regularization with a second view, and semi-supervised learning on real data.