In the past few years, Convolutional Neural Networks (CNNs) have been achieving state-of-the-art performance on a variety of problems. Many companies employ resources and money to generate these models and provide them as an API, therefore it is in their best interest to protect them, i.e., to avoid that someone else copies them. Recent studies revealed that state-of-the-art CNNs are vulnerable to adversarial examples attacks, and this weakness indicates that CNNs do not need to operate in the problem domain (PD). Therefore, we hypothesize that they also do not need to be trained with examples of the PD in order to operate in it. Given these facts, in this paper, we investigate if a target black-box CNN can be copied by persuading it to confess its knowledge through random non-labeled data. The copy is two-fold: i) the target network is queried with random data and its predictions are used to create a fake dataset with the knowledge of the network; and ii) a copycat network is trained with the fake dataset and should be able to achieve similar performance as the target network. This hypothesis was evaluated locally in three problems (facial expression, object, and crosswalk classification) and against a cloud-based API. In the copy attacks, images from both non-problem domain and PD were used. All copycat networks achieved at least 93.7% of the performance of the original models with non-problem domain data, and at least 98.6% using additional data from the PD. Additionally, the copycat CNN successfully copied at least 97.3% of the performance of the Microsoft Azure Emotion API. Our results show that it is possible to create a copycat CNN by simply querying a target network as black-box with random non-labeled data.

Indeed, the bulk of the empirical academic literature in finance takes this approach. However, practitioners' use of models, in particular for the pricing and risk management of derivative financial products relative to observed prices for liquidly traded market instruments, typically tends to depart from this ideal. Primacy is accorded to model "calibration" over empirical consistency, i.e., choosing a set of liquidly traded market instruments (which may include liquidly traded derivatives) as "calibration instruments", model parameters are determined so as to match model prices of these instruments as closely as possible to observed market prices at a given point in time. Once these market prices have changed, the model parameters (which were assumed to be constant, or at most time-varying in a known deterministic fashion) are recalibrated, thereby contradicting the model assumptions. "Legalising" these parameter changes by expanding the state space (e.g. via regime-switching or stochastic volatility models) shifts, rather than resolves, the problem: for example in the case of stochastic volatility, volatility becomes a state variable rather than a model parameter, and can evolve stochastically, but the parameters of the stochastic volatility process itself are assumed to be time-invariant.

In this paper, we propose a novel reinforcement- learning algorithm consisting in a stochastic variance-reduced version of policy gradient for solving Markov Decision Processes (MDPs). Stochastic variance-reduced gradient (SVRG) methods have proven to be very successful in supervised learning. However, their adaptation to policy gradient is not straightforward and needs to account for I) a non-concave objective func- tion; II) approximations in the full gradient com- putation; and III) a non-stationary sampling pro- cess. The result is SVRPG, a stochastic variance- reduced policy gradient algorithm that leverages on importance weights to preserve the unbiased- ness of the gradient estimate. Under standard as- sumptions on the MDP, we provide convergence guarantees for SVRPG with a convergence rate that is linear under increasing batch sizes. Finally, we suggest practical variants of SVRPG, and we empirically evaluate them on continuous MDPs.

We investigate learning of the differential geometric structure of a data manifold embedded in a high-dimensional Euclidean space. We first analyze kernel-based algorithms and show that under the usual regularizations, non-probabilistic methods cannot recover the differential geometric structure, but instead find mostly linear manifolds or spaces equipped with teleports. To properly learn the differential geometric structure, non-probabilistic methods must apply regularizations that enforce large gradients, which go against common wisdom. We repeat the analysis for probabilistic methods and find that under reasonable priors, the geometric structure can be recovered. Fully exploiting the recovered structure, however, requires the development of stochastic extensions to classic Riemannian geometry. We take early steps in that regard. Finally, we partly extend the analysis to modern models based on neural networks, thereby highlighting geometric and probabilistic shortcomings of current deep generative models.

This paper proposes a new method for solving the well-known rank aggregation problem from pairwise comparisons using the method of low-rank matrix completion. The partial and noisy data of pairwise comparisons is transformed into a matrix form. We then use tools from matrix completion, which has served as a major component in the low-rank completion solution of the Netflix challenge, to construct the preference of the different objects. In our approach, the data of multiple comparisons is used to create an estimate of the probability of object i to win (or be chosen) over object j, where only a partial set of comparisons between N objects is known. The data is then transformed into a matrix form for which the noiseless solution has a known rank of one. An alternating minimization algorithm, in which the target matrix takes a bilinear form, is then used in combination with maximum likelihood estimation for both factors. The reconstructed matrix is used to obtain the true underlying preference intensity. This work demonstrates the improvement of our proposed algorithm over the current state-of-the-art in both simulated scenarios and real data.

We consider stochastic gradient descent for binary classification problems in a reproducing kernel Hilbert space. In traditional analysis, it is known that the expected classification error converges more slowly than the expected risk even when assuming a low-noise condition on the conditional label probabilities. Consequently, the resulting rate is sublinear. Therefore, it is important to consider whether much faster convergence of the expected classification error can be achieved. In recent research, an exponential convergence rate for stochastic gradient descent was shown under a strong low-noise condition, but theoretical analysis of this was limited to the square loss function, which is somewhat inadequate for binary classification tasks. In this paper, we show an exponential convergence rate of the expected classification error in the final phase of learning for a wide class of differentiable convex loss functions under similar assumptions.

This paper develops a computationally efficient posterior sampling algorithm for Bayesian linear regression models with Gaussian errors. Our new approach is motivated by the fact that existing software implementations for Bayesian linear regression do not readily handle problems with large number of observations (hundreds of thousands) and predictors (thousands). Moreover, existing sampling algorithms for popular shrinkage priors are bespoke Gibbs samplers based on case-specific latent variable representations. By contrast, the new algorithm does not rely on case-specific auxiliary variable representations, which allows for rapid prototyping of novel shrinkage priors outside the conditionally Gaussian framework. Specifically, we propose a slice-within-Gibbs sampler based on the elliptical slice sampler of Murray et al. [2010].

The implementation of optimal power flow (OPF) methods to perform voltage and power flow regulation in electric networks is generally believed to require communication. We consider distribution systems with multiple controllable Distributed Energy Resources (DERs) and present a data-driven approach to learn control policies for each DER to reconstruct and mimic the solution to a centralized OPF problem from solely locally available information. Collectively, all local controllers closely match the centralized OPF solution, providing near-optimal performance and satisfaction of system constraints. A rate distortion framework facilitates the analysis of how well the resulting fully decentralized control policies are able to reconstruct the OPF solution. Our methodology provides a natural extension to decide what buses a DER should communicate with to improve the reconstruction of its individual policy. The method is applied on both single- and three-phase test feeder networks using data from real loads and distributed generators. It provides a framework for Distribution System Operators to efficiently plan and operate the contributions of DERs to active distribution networks.

Our goal is to synthesize controllers for robots that provably generalize well to novel environments given a dataset of example environments. The key technical idea behind our approach is to leverage tools from generalization theory in machine learning by exploiting a precise analogy (which we present in the form of a reduction) between robustness of controllers to novel environments and generalization of hypotheses in supervised learning. In particular, we utilize the Probably Approximately Correct (PAC)-Bayes framework, which allows us to obtain upper bounds (that hold with high probability) on the expected cost of (stochastic) controllers across novel environments. We propose control synthesis algorithms that explicitly seek to minimize this upper bound. The corresponding optimization problem can be solved using convex optimization (Relative Entropy Programming in particular) in the setting where we are optimizing over a finite control policy space. In the more general setting of continuously parameterized controllers, we minimize this upper bound using stochastic gradient descent. We present examples of our approach in the context of obstacle avoidance control with depth measurements. Our simulated examples demonstrate the potential of our approach to provide strong generalization guarantees on controllers for robotic systems with continuous state and action spaces, complicated (e.g., nonlinear) dynamics, and rich sensory inputs (e.g., depth measurements).

Random weights in convolutional neural networks have shown promising results in previous studies yet remain below par compared to trained networks on image benchmarks. We explore depthwise convolutional neural networks with thousands of random filters in each layer, the sign activation function in between layers, and training performed only at the last layer with a linear support vector machine. We show that our network attains higher accuracies than previous random networks and is comparable to trained large networks on large images from the STL10 and ImageNet benchmarks. Since our network lacks a gradient due to the sign activation it is not possible to produce gradient-based adversarial examples targeting it. We show that our network is also less affected by gradient based adversarial examples produced from state of the art networks that considerably hamper their performance. As a possible explanation for our network's accuracy with random weights we show that the the margin of the linear support vector machine is larger on our final representation compared to the original dataset and increases with the number of random filters. Our network is simple and fast to train and predict, attains high classification accuracy particularly on large images, is hard to attack with adversarial examples, and is less affected by gradient based adversarial examples compared to state of the art networks.