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.

Learning reduced component representations of data using nonlinear transformations is a central problem in unsupervised learning with a rich history. Recently, a new family of algorithms based on maximum likelihood optimization with change of variables has demonstrated an impressive ability to model complex nonlinear data distributions. These algorithms learn to map from arbitrary random variables to independent components using invertible nonlinear function approximators. Despite the potential of this framework, the underlying optimization objective is ill-posed for a large class of variables, inhibiting accurate component estimates in many use cases. We present a new Tikhonov regularization technique for nonlinear independent component estimation that mediates the instability of the algorithm and facilitates robust component estimates. In addition, we provide a theoretically grounded procedure for feature extraction that produces PCA-like representations of nonlinear distributions using the learned model. We apply our technique to a handful of nonlinear data manifolds and show that the resulting representations possess important consistencies lacked by unregularized models.

It is obvious that there are significant differences between groups (i.e.

Learning representation has been proven to be helpful in numerous machine learning tasks. The success of the majority of existing representation learning approaches often requires a large amount of consistent and noise-free labels. However, labels are not accessible in many real-world scenarios and they are usually annotated by the crowds. In practice, the crowdsourced labels are usually inconsistent among crowd workers given their diverse expertise and the number of crowdsourced labels is very limited. Thus, directly adopting crowdsourced labels for existing representation learning algorithms is inappropriate and suboptimal. In this paper, we investigate the above problem and propose a novel framework of \textbf{R}epresentation \textbf{L}earning with crowdsourced \textbf{L}abels, i.e., "RLL", which learns representation of data with crowdsourced labels by jointly and coherently solving the challenges introduced by limited and inconsistent labels. The proposed representation learning framework is evaluated in two real-world education applications. The experimental results demonstrate the benefits of our approach on learning representation from limited labeled data from the crowds, and show RLL is able to outperform state-of-the-art baselines. Moreover, detailed experiments are conducted on RLL to fully understand its key components and the corresponding performance.

In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme values for certain subgroups $\alpha$ $\subset$ {1,. .. , d} of variables Xj. Under the heavy-tail assumption, which is precisely appropriate for modeling these phenomena, statistical methods relying on multivariate extreme value theory have been developed in the past few years for identifying such events/subgroups. This paper exploits this approach much further by means of a novel mixture model that permits to describe the distribution of extremal observations and where the anomaly type $\alpha$ is viewed as a latent variable. One may then take advantage of the model by assigning to any extreme point a posterior probability for each anomaly type $\alpha$, defining implicitly a similarity measure between anomalies. It is explained at length how the latter permits to cluster extreme observations and obtain an informative planar representation of anomalies using standard graph-mining tools. The relevance and usefulness of the clustering and 2-d visual display thus designed is illustrated on simulated datasets and on real observations as well, in the aeronautics application domain.

Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is challenging due to the high dimensionality of the parameter space. In this paper, we construct low-dimensional subspaces of parameter space, such as the first principal components of the stochastic gradient descent (SGD) trajectory, which contain diverse sets of high performing models. In these subspaces, we are able to apply elliptical slice sampling and variational inference, which struggle in the full parameter space. We show that Bayesian model averaging over the induced posterior in these subspaces produces accurate predictions and well calibrated predictive uncertainty for both regression and image classification.

Gaussian processes are expressive, non-parametric statistical models that are well-suited to learn nonlinear dynamical systems. However, large-scale inference in these state space models is a challenging problem. In this paper, we propose CBF-SSM a scalable model that employs a structured variational approximation to maintain temporal correlations. In contrast to prior work, our approach applies to the important class of unstable systems, where state uncertainty grows unbounded over time. For these systems, our method contains a probabilistic, model-based backward pass that infers latent states during training. We demonstrate state-of-the-art performance in our experiments. Moreover, we show that CBF-SSM can be combined with physical models in the form of ordinary differential equations to learn a reliable model of a physical flying robotic vehicle.

In recent years, the use of data-driven modelling and integration of behavioural and psychological factors in discrete choice and travel behaviour analysis have become active areas of research [2, 3, 4]. In the context of data-driven models, behavioural variations describe the correlation between observed choice attributes and unobserved socioeconomic factors using a flexible and tractable model specification. These variations include: decision-protocols, choice sets, unobserved taste variations and unobserved attributes [5]. Under these considerations, recent studies on travel behaviour analysis have so far primarily focused on representing heterogeneity in the error correction function and incorporating it into utility based multinomial logit (MNL) models [3]. Models such as mixed multinomial logit (MMNL) or latent class (LC) model offers flexibility in representing heterogeneity and substitution patterns. In addition, recent conceptual frameworks such as the integrated choice and latent variable (ICLV) use individuals' psychometric indicators to represent unobserved behavioural and perception heterogeneity [6]. It is also possible to apply a generative machine learning to identify informative latent constructs in travel decision making without subjective behaviour indicators [7, 8]. However, the true underlying behavioural patterns are often unknown and usually approximated by some predetermined exogenous indicator variables that would often lead to model misspecification due to lack of complete information, or error in data collection [9]. Furthermore, accurate specification of the underlying distribution assumes individuals have access to all available information regarding the travel activity (e.g.

We offer a graphical interpretation of unfairness in a dataset as the presence of an unfair causal path in the causal Bayesian network representing the data-generation mechanism. We use this viewpoint to revisit the recent debate surrounding the COMPAS pretrial risk assessment tool and, more generally, to point out that fairness evaluation on a model requires careful considerations on the patterns of unfairness underlying the training data. We show that causal Bayesian networks provide us with a powerful tool to measure unfairness in a dataset and to design fair models in complex unfairness scenarios.

In this paper, we consider sequential online prediction (SOP) for streaming data in the presence of outliers and change points. We propose an INstant TEmporal structure Learning (INTEL) algorithm to address this problem.Our INTEL algorithm is developed based on a full consideration to the duality between online prediction and anomaly detection. We first employ a mixture of weighted GP models (WGPs) to cover the expected possible temporal structures of the data. Then, on the basis of the rich modeling capacity of this WGP mixture, we develop an efficient technique to instantly learn (capture) the temporal structure of the data that follows a regime shift. This instant learning is achieved only by adjusting one hyper-parameter value of the mixture model. A weighted generalization of the product of experts (POE) model is used for fusing predictions yielded from multiple GP models. An outlier is declared once a real observation seriously deviates from the fused prediction. If a certain number of outliers are consecutively declared, then a change point is declared. Extensive experiments are performed using a diverse of real datasets. Results show that the proposed algorithm is significantly better than benchmark methods for SOP in the presence of outliers and change points.