As algorithms are increasingly used to make important decisions that affect human lives, ranging from social benefit assignment to predicting risk of criminal recidivism, concerns have been raised about the fairness of algorithmic decision making. Most prior works on algorithmic fairness normatively prescribe how fair decisions ought to be made. In contrast, here, we descriptively survey users for how they perceive and reason about fairness in algorithmic decision making. A key contribution of this work is the framework we propose to understand why people perceive certain features as fair or unfair to be used in algorithms. Our framework identifies eight properties of features, such as relevance, volitionality and reliability, as latent considerations that inform people's moral judgments about the fairness of feature use in decision-making algorithms. We validate our framework through a series of scenario-based surveys with 576 people. We find that, based on a person's assessment of the eight latent properties of a feature in our exemplar scenario, we can accurately (> 85%) predict if the person will judge the use of the feature as fair. Our findings have important implications. At a high-level, we show that people's unfairness concerns are multi-dimensional and argue that future studies need to address unfairness concerns beyond discrimination. At a low-level, we find considerable disagreements in people's fairness judgments. We identify root causes of the disagreements, and note possible pathways to resolve them.

We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.

In regression analysis, curve fitting is the process of specifying the model that provides the best fit to the specific curves in your dataset. Curved relationships between variables are not as straightforward to fit and interpret as linear relationships.

We study the bias of generic optimization methods, including Mirror Descent, Natural Gradient Descent and Steepest Descent with respect to different potentials and norms, when optimizing underdetermined linear regression or separable linear classification problems. We ask the question of whether the global minimum (among the many possible global minima) reached by optimization algorithms can be characterized in terms of the potential or norm, and independently of hyperparameter choices such as step size and momentum.

Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by several studies. However, one of the biggest issues in sparse regularization is that its performance is quite sensitive to correlations between features. Ordinary $\ell_1$ regularization can select variables correlated with each other, which results in deterioration of not only its generalization error but also interpretability. In this paper, we propose a new regularization method, "Independently Interpretable Lasso" (IILasso). Our proposed regularizer suppresses selecting correlated variables, and thus each active variable independently affects the objective variable in the model. Hence, we can interpret regression coefficients intuitively and also improve the performance by avoiding overfitting. We analyze theoretical property of IILasso and show that the proposed method is much advantageous for its sign recovery and achieves almost minimax optimal convergence rate. Synthetic and real data analyses also indicate the effectiveness of IILasso.

The $L_1$-regularized models are widely used for sparse regression or classification tasks. In this paper, we propose the orthant-wise passive descent algorithm (OPDA) for optimizing $L_1$-regularized models, as an improved substitute of proximal algorithms, which are the standard tools for optimizing the models nowadays. OPDA uses a stochastic variance-reduced gradient (SVRG) to initialize the descent direction, then apply a novel alignment operator to encourage each element keeping the same sign after one iteration of update, so the parameter remains in the same orthant as before. It also explicitly suppresses the magnitude of each element to impose sparsity. The quasi-Newton update can be utilized to incorporate curvature information and accelerate the speed. We prove a linear convergence rate for OPDA on general smooth and strongly-convex loss functions. By conducting experiments on $L_1$-regularized logistic regression and convolutional neural networks, we show that OPDA outperforms state-of-the-art stochastic proximal algorithms, implying a wide range of applications in training sparse models.

In the last blog post of this series, we discussed classifiers. The categories of classifiers and how they are evaluated were discussed. We have also discussed regression models in depth. In this post, we dwell a little deeper in how regression models can be used for classification tasks. Logistic Regression is a widely used regression model used for classification tasks.

Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have limited representational power. We present the Gaussian Process Autoregressive Regression (GPAR) model, a scalable multi-output GP model that is able to capture nonlinear, possibly input-varying, dependencies between outputs in a simple and tractable way: the product rule is used to decompose the joint distribution over the outputs into a set of conditionals, each of which is modelled by a standard GP. GPAR's efficacy is demonstrated on a variety of synthetic and real-world problems, outperforming existing GP models and achieving state-of-the-art performance on the tasks with existing benchmarks.

This is the first article of a multi-part series on using Python and Machine Learning to build models to predict weather temperatures based off data collected from Weather Underground. The series will be comprised of three different articles describing the major aspects of a Machine Learning project. The data used in this series will be collected from Weather Underground's free tier API web service. I will be using the requests library to interact with the API to pull in weather data since 2015 for the city of Lincoln, Nebraska. Once collected, the data will need to be process and aggregated into a format that is suitable for data analysis, and then cleaned. The second article will focus on analyzing the trends in the data with the goal of selecting appropriate features for building a Linear Regression model using the statsmodels and scikit-learn Python libraries. I will discuss the importance of understanding the assumptions necessary for using a Linear Regression model and demonstrate how to evaluate the features to build a robust model.

Hyperparameters are critical in machine learning, as different hyperparameters often result in models with significantly different performance. Hyperparameters may be deemed confidential because of their commercial value and the confidentiality of the proprietary algorithms that the learner uses to learn them. In this work, we propose attacks on stealing the hyperparameters that are learned by a learner. We call our attacks hyperparameter stealing attacks. Our attacks are applicable to a variety of popular machine learning algorithms such as ridge regression, logistic regression, support vector machine, and neural network. We evaluate the effectiveness of our attacks both theoretically and empirically. For instance, we evaluate our attacks on Amazon Machine Learning. Our results demonstrate that our attacks can accurately steal hyperparameters. We also study countermeasures. Our results highlight the need for new defenses against our hyperparameter stealing attacks for certain machine learning algorithms.