As one of my colleagues pointed out in her recent blog, "140 years later, what do we know about customer service?", the invention of the telephone in 1876 -- and the subsequent invention of the switchboard in 1894 – ushered in the era of modern telecommunications and provided consumers with a way to more easily voice their concerns to companies with whom they do business. Ever since, companies have been looking for better ways to handle customer care. One of the biggest challenges for communications service providers (CSPs) has been the lack of specific information about the customer who's calling with an issue; their service, their location, their equipment. However, given recent advances, this no longer needs to be a challenge. Thanks to a variety of different analytics applications, when customers call the help desk of their local CSP, customer service representatives (CSRs) are now able to access quite a bit of client-specific information, including the type of access point found in the home, the settings of that device, what network equipment they connect to for service and more.

Recurrent neural networks are a type of neural network where the outputs from previous time steps are fed as input to the current time step. This creates a network graph or circuit diagram with cycles, which can make it difficult to understand how information moves through the network. In this post, you will discover the concept of unrolling or unfolding recurrent neural networks. Recurrent neural networks are a type of neural network where outputs from previous time steps are taken as inputs for the current time step. We can demonstrate this with a picture.

Networks capture pairwise interactions between entities and are frequently used in applications such as social networks, food networks, and protein interaction networks, to name a few. Communities, cohesive groups of nodes, often form in these applications, and identifying them gives insight into the overall organization of the network. One common quality function used to identify community structure is modularity. In Hu et al. [SIAM J. App. Math., 73(6), 2013], it was shown that modularity optimization is equivalent to minimizing a particular nonconvex total variation (TV) based functional over a discrete domain. They solve this problem---assuming the number of communities is known---using a Merriman, Bence, Osher (MBO) scheme. We show that modularity optimization is equivalent to minimizing a convex TV-based functional over a discrete domain---again, assuming the number of communities is known. Furthermore, we show that modularity has no convex relaxation satisfying certain natural conditions. Despite this, we partially relax the discrete constraint using a Ginzburg Landau functional, yielding an optimization problem that is more nearly convex. We then derive an MBO algorithm with fewer parameters than in Hu et al. and which is 7 times faster at solving the associated diffusion equation due to the fact that the underlying discretization is unconditionally stable. Our numerical tests include a hyperspectral video whose associated graph has 29 million edges, which is roughly 37 times larger than was handled in the paper of Hu et al.

We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing point approximation that is well-tailored to the convolutional kernel. This allows us to gain the generalisation benefit of a convolutional kernel, together with fast but accurate posterior inference. We investigate several variations of the convolutional kernel, and apply it to MNIST and CIFAR-10, which have both been known to be challenging for Gaussian processes. We also show how the marginal likelihood can be used to find an optimal weighting between convolutional and RBF kernels to further improve performance. We hope that this illustration of the usefulness of a marginal likelihood will help automate discovering architectures in larger models.

The presence of missing entries in data often creates challenges for pattern recognition algorithms. Traditional algorithms for clustering data assume that all the feature values are known for every data point. We propose a method to cluster data in the presence of missing information. Unlike conventional clustering techniques where every feature is known for each point, our algorithm can handle cases where a few feature values are unknown for every point. For this more challenging problem, we provide theoretical guarantees for clustering using a $\ell_0$ fusion penalty based optimization problem. Furthermore, we propose an algorithm to solve a relaxation of this problem using saturating non-convex fusion penalties. It is observed that this algorithm produces solutions that degrade gradually with an increase in the fraction of missing feature values. We demonstrate the utility of the proposed method using a simulated dataset, the Wine dataset and also an under-sampled cardiac MRI dataset. It is shown that the proposed method is a promising clustering technique for datasets with large fractions of missing entries.

We prove an exact relationship between the optimal denoising function and the data distribution in the case of additive Gaussian noise, showing that denoising implicitly models the structure of data allowing it to be exploited in the unsupervised learning of representations. This result generalizes a known relationship [2], which is valid only in the limit of small corruption noise.

A composite loss framework is proposed for low-rank modeling of data consisting of interesting and common values, such as excess zeros or missing values. The methodology is motivated by the generalized low-rank framework and the hurdle method which is commonly used to analyze zero-inflated counts. The model is demonstrated on a manufacturing data set and applied to the problem of missing value imputation.

Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the concept of an asymptotically linear estimator and the associated influence function leads to optimal sampling procedures for a wide class of popular models. Furthermore, for linear regression models which have well-studied procedures for non-uniform sub-sampling, we show our optimal influence function based method outperforms previous approaches. We empirically show the improved performance of our method on real datasets.

Célia Châtel Aix-Marseille University, France Pierre Geurts University of Liège, Belgium Dealing with datasets of very high dimension is a major challenge in machine learning. In this paper, we consider the problem of feature selection in applications where the memory is not large enough to contain all features. In this setting, we propose a novel tree-based feature selection approach that builds a sequence of randomized trees on small subsamples of variables mixing both variables already identified as relevant by previous models and variables randomly selected among the other variables. As our main contribution, we provide an in-depth theoretical analysis of this method in infinite sample setting. In particular, we study its soundness with respect to common definitions of feature relevance and its convergence speed under various variable dependance scenarios. We also provide some preliminary empirical results highlighting the potential of the approach.

We consider the problem of bandit optimization, inspired by stochastic optimization and online learning problems with bandit feedback. In this problem, the objective is to minimize a global loss function of all the actions, not necessarily a cumulative loss. This framework allows us to study a very general class of problems, with applications in statistics, machine learning, and other fields. To solve this problem, we analyze the Upper-Confidence Frank-Wolfe algorithm, inspired by techniques for bandits and convex optimization. We give theoretical guarantees for the performance of this algorithm over various classes of functions, and discuss the optimality of these results.