Shifting Regret, Mirror Descent, and Matrices

We consider the problem of online prediction in changing environments. In this framework the performance of a predictor is evaluated as the loss relative to an arbitrarily changing predictor, whose individual components come from a base class of predictors. Typical results in the literature consider different base classes (experts, linear predictors on the simplex, etc.) separately. Introducing an arbitrary mapping inside the mirror decent algorithm, we provide a framework that unifies and extends existing results. As an example, we prove new shifting regret bounds for matrix prediction problems

Classification with Margin Constraints: A Unification with Applications to Optimization

This paper introduces Classification with Margin Constraints (CMC), a simple generalization of cost-sensitive classification that unifies several learning settings. In particular, we show that a CMC classifier can be used, out of the box, to solve regression, quantile estimation, and several anomaly detection formulations. On the one hand, our reductions to CMC are at the loss level: the optimization problem to solve under the equivalent CMC setting is exactly the same as the optimization problem under the original (e.g. regression) setting. On the other hand, due to the close relationship between CMC and standard binary classification, the ideas proposed for efficient optimization in binary classification naturally extend to CMC. As such, any improvement in CMC optimization immediately transfers to the domains reduced to CMC, without the need for new derivations or programs. To our knowledge, this unified view has been overlooked by the existing practice in the literature, where an optimization technique (such as SMO or PEGASOS) is first developed for binary classification and then extended to other problem domains on a case-by-case basis. We demonstrate the flexibility of CMC by reducing two recent anomaly detection and quantile learning methods to CMC

SDP Relaxation with Randomized Rounding for Energy Disaggregation

We develop a scalable, computationally efficient method for the task of energy disaggregation for home appliance monitoring. In this problem the goal is to estimate the energy consumption of each appliance over time based on the total energy-consumption signal of a household. The current state of the art is to model the problem as inference in factorial HMMs, and use quadratic programming to find an approximate solution to the resulting quadratic integer program. Here we take a more principled approach, better suited to integer programming problems, and find an approximate optimum by combining convex semidefinite relaxations randomized rounding, as well as a scalable ADMM method that exploits the special structure of the resulting semidefinite program. Simulation results both in synthetic and real-world datasets demonstrate the superiority of our method

(Bandit) Convex Optimization with Biased Noisy Gradient Oracles

For bandit convex optimization we propose a model, where a gradient estimation oracle acts as an intermediary between a noisy function evaluation oracle and the algorithms. The algorithms can control the bias-variance tradeoff in the gradient estimates. We prove lower and upper bounds for the minimax error of algorithms that interact with the objective function by controlling this oracle. The upper bounds replicate many existing results (capturing the essence of existing proofs) while the lower bounds put a limit on the achievable performance in this setup. In particular, our results imply that no algorithm can achieve the optimal minimax error rate in stochastic bandit smooth convex optimization

Following the Leader and Fast Rates in Linear Prediction: Curved Constraint Sets and Other Regularities

The follow the leader (FTL) algorithm, perhaps the simplest of all online learning algorithms, is known to perform well when the loss functions it is used on are positively curved. In this paper we ask whether there are other “lucky” settings when FTL achieves sublinear, “small” regret. In particular, we study the fundamental problem of linear prediction over a non-empty convex, compact domain. Amongst other results, we prove that the curvature of the boundary of the domain can act as if the losses were curved: In this case, we prove that as long as the mean of the loss vectors have positive lengths bounded away from zero, FTL enjoys a logarithmic growth rate of regret, while, e.g., for polyhedral domains and stochastic data it enjoys finite expected regret. Building on a previously known meta-algorithm, we also get an algorithm that simultaneously enjoys the worst-case guarantees and the bound available for FTL

Following the Leader and Fast Rates in Linear Prediction: Curved Constraint Sets and Other Regularities

The follow the leader (FTL) algorithm, perhaps the simplest of all online learning algorithms, is known to perform well when the loss functions it is used on are positively curved. In this paper we ask whether there are other “lucky” settings when FTL achieves sublinear, “small” regret. In particular, we study the fundamental problem of linear prediction over a non-empty convex, compact domain. Amongst other results, we prove that the curvature of the boundary of the domain can act as if the losses were curved: In this case, we prove that as long as the mean of the loss vectors have positive lengths bounded away from zero, FTL enjoys a logarithmic growth rate of regret, while, e.g., for polyhedral domains and stochastic data it enjoys finite expected regret. Building on a previously known meta-algorithm, we also get an algorithm that simultaneously enjoys the worst-case guarantees and the bound available for FTL

SDP Relaxation with Randomized Rounding for Energy Disaggregation

We develop a scalable, computationally efficient method for the task of energy disaggregation for home appliance monitoring. In this problem the goal is to estimate the energy consumption of each appliance over time based on the total energy-consumption signal of a household. The current state of the art is to model the problem as inference in factorial HMMs, and use quadratic programming to find an approximate solution to the resulting quadratic integer program. Here we take a more principled approach, better suited to integer programming problems, and find an approximate optimum by combining convex semidefinite relaxations randomized rounding, as well as a scalable ADMM method that exploits the special structure of the resulting semidefinite program. Simulation results both in synthetic and real-world datasets demonstrate the superiority of our method

Simultaneous mesoscopic and two-photon imaging of neuronal activity in cortical circuits.

Spontaneous and sensory-evoked activity propagates across varying spatial scales in the mammalian cortex, but technical challenges have limited conceptual links between the function of local neuronal circuits and brain-wide network dynamics. We present a method for simultaneous cellular-resolution two-photon calcium imaging of a local microcircuit and mesoscopic widefield calcium imaging of the entire cortical mantle in awake mice. Our multi-scale approach involves a microscope with an orthogonal axis design where the mesoscopic objective is oriented above the brain and the two-photon objective is oriented horizontally, with imaging performed through a microprism. We also introduce a viral transduction method for robust and widespread gene delivery in the mouse brain. These approaches allow us to identify the behavioral state-dependent functional connectivity of pyramidal neurons and vasoactive intestinal peptide-expressing interneurons with long-range cortical networks. Our imaging system provides a powerful strategy for investigating cortical architecture across a wide range of spatial scales

Laser-induced chemical transformation of freestanding graphene oxide membranes in liquid and gas ammonia environments

Laser-induced chemical conversion of graphene oxide (GO) is an effective way to modify its properties and expand its potential use for numerous applications. In this work, a mechanically stable and flexible free-standing GO membrane is synthesized and further processed by ultraviolet laser radiation in gas and liquid ammonia-rich environments. Electron and atomic force microscopy, as well as X-ray photoelectron spectroscopy analysis, reveal that laser irradiation in gas leads to a large defect-induced morphology modification and high deoxygenation process, accompanied by the slight incorporation of nitrogen functionality to the reduced GO structure. Conversely, irradiation in liquid provokes significant integration of nitrogen groups, essentially amines, into a partially reduced GO structure, without evident modification of the morphology. Electrical measurements on the macro- and nano-scale point to a complex contribution of morphology and oxidized regions to the overall resistance of the rGO.The authors acknowledge the financial support of the Spanish Ministry of Economy and Competitiveness under the project ENE2014-56109-C3-3-R, in addition to the Romanian National Authority for Scientific Research and Innovation, CNCS – UEFISCDI, under the Grants PN-II-ID-PCE-2012-4-0292 and PNII- RU-TE-2014-4-1194. ICMAB acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the “Severo Ochoa” Programme for Centres of Excellence in R&D (SEV-2015-0496).Peer reviewe