Primal-Dual Rates and Certificates

We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in particular in machine learning applications. We obtain new primal-dual convergence rates, e.g., for the Lasso as well as many L1, Elastic Net, group Lasso and TV-regularized problems. The theory applies to any norm-regularized generalized linear model. Our approach provides efficiently computable duality gaps which are globally defined, without modifying the original problems in the region of interest.Comment: appearing at ICML 2016 - Proceedings of the 33rd International Conference on Machine Learning, New York, NY, USA, 2016. JMLR: W&CP volume 4

Scalable and interpretable product recommendations via overlapping co-clustering

We consider the problem of generating interpretable recommendations by identifying overlapping co-clusters of clients and products, based only on positive or implicit feedback. Our approach is applicable on very large datasets because it exhibits almost linear complexity in the input examples and the number of co-clusters. We show, both on real industrial data and on publicly available datasets, that the recommendation accuracy of our algorithm is competitive to that of state-of-art matrix factorization techniques. In addition, our technique has the advantage of offering recommendations that are textually and visually interpretable. Finally, we examine how to implement our technique efficiently on Graphical Processing Units (GPUs).Comment: In IEEE International Conference on Data Engineering (ICDE) 201

Performative Prediction: Past and Future

Predictions in the social world generally influence the target of prediction, a phenomenon known as performativity. Self-fulfilling and self-negating predictions are examples of performativity. Of fundamental importance to economics, finance, and the social sciences, the notion has been absent from the development of machine learning. In machine learning applications, performativity often surfaces as distribution shift. A predictive model deployed on a digital platform, for example, influences consumption and thereby changes the data-generating distribution. We survey the recently founded area of performative prediction that provides a definition and conceptual framework to study performativity in machine learning. A consequence of performative prediction is a natural equilibrium notion that gives rise to new optimization challenges. Another consequence is a distinction between learning and steering, two mechanisms at play in performative prediction. The notion of steering is in turn intimately related to questions of power in digital markets. We review the notion of performative power that gives an answer to the question how much a platform can steer participants through its predictions. We end on a discussion of future directions, such as the role that performativity plays in contesting algorithmic systems

Redshift-space limits of bound structures

An exponentially expanding Universe, possibly governed by a cosmological constant, forces gravitationally bound structures to become more and more isolated, eventually becoming causally disconnected from each other and forming so-called "island universes". This new scenario reformulates the question about which will be the largest structures that will remain gravitationally bound, together with requiring a systematic tool that can be used to recognize the limits and mass of these structures from observational data, namely redshift surveys of galaxies. Here we present a method, based on the spherical collapse model and N-body simulations, by which we can estimate the limits of bound structures as observed in redshift space. The method is based on a theoretical criterion presented in a previous paper that determines the mean density contrast that a spherical shell must have in order to be marginally bound to the massive structure within it. Understanding the kinematics of the system, we translated the real-space limiting conditions of this "critical" shell to redshift space, producing a projected velocity envelope that only depends on the density profile of the structure. From it we created a redshift-space version of the density contrast that we called "density estimator", which can be calibrated from N-body simulations for a reasonable projected velocity envelope template, and used to estimate the limits and mass of a structure only from its redshift-space coordinates.Comment: Contains 12 pages, 12 figures and 8 table