The cost of computing the spectrum of Laplacian matrices hinders the application of spectral clustering to large data sets. While approximations recover computational tractability, they can potentially affect clustering performance. This paper proposes a practical approach to learn spectral clustering based on adaptive stochastic gradient optimization. Crucially, the proposed approach recovers the exact spectrum of Laplacian matrices in the limit of the iterations, and the cost of each iteration is linear in the number of samples. Extensive experimental validation on data sets with up to half a million samples demonstrate its scalability and its ability to outperform state-of-the-art approximate methods to learn spectral clustering for a given computational budget.

Classification is the task of predicting the class labels of objects based on the observation of their features. In contrast, quantification has been defined as the task of determining the prevalences of the different sorts of class labels in a target dataset. The simplest approach to quantification is Classify & Count where a classifier is optimised for classification on a training set and applied to the target dataset for the prediction of class labels. In the case of binary quantification, the number of predicted positive labels is then used as an estimate of the prevalence of the positive class in the target dataset. Since the performance of Classify & Count for quantification is known to be inferior its results typically are subject to adjustments. However, some researchers recently have suggested that Classify & Count might actually work without adjustments if it is based on a classifer that was specifically trained for quantification. We discuss the theoretical foundation for this claim and explore its potential and limitations with a numerical example based on the binormal model with equal variances. In order to identify an optimal quantifier in the binormal setting, we introduce the concept of local Bayes optimality. As a side remark, we present a complete proof of a theorem by Ye et al. (2012).

Control of non-episodic, finite-horizon dynamical systems with uncertain dynamics poses a tough and elementary case of the exploration-exploitation trade-off. Bayesian reinforcement learning, reasoning about the effect of actions and future observations, offers a principled solution, but is intractable. We review, then extend an old approximate approach from control theory---where the problem is known as dual control---in the context of modern regression methods, specifically generalized linear regression. Experiments on simulated systems show that this framework offers a useful approximation to the intractable aspects of Bayesian RL, producing structured exploration strategies that differ from standard RL approaches. We provide simple examples for the use of this framework in (approximate) Gaussian process regression and feedforward neural networks for the control of exploration.

We propose and analyze an alternate approach to off-policy multi-step temporal difference learning, in which off-policy returns are corrected with the current Q-function in terms of rewards, rather than with the target policy in terms of transition probabilities. We prove that such approximate corrections are sufficient for off-policy convergence both in policy evaluation and control, provided certain conditions. These conditions relate the distance between the target and behavior policies, the eligibility trace parameter and the discount factor, and formalize an underlying tradeoff in off-policy TD($\lambda$). We illustrate this theoretical relationship empirically on a continuous-state control task.

A major contributing factor to the recent advances in deep neural networks is structural units that let sensory information and gradients to propagate easily. Gating is one such structure that acts as a flow control. Gates are employed in many recent state-of-the-art recurrent models such as LSTM and GRU, and feedforward models such as Residual Nets and Highway Networks. This enables learning in very deep networks with hundred layers and helps achieve record-breaking results in vision (e.g., ImageNet with Residual Nets) and NLP (e.g., machine translation with GRU). However, there is limited work in analysing the role of gating in the learning process. In this paper, we propose a flexible $p$-norm gating scheme, which allows user-controllable flow and as a consequence, improve the learning speed. This scheme subsumes other existing gating schemes, including those in GRU, Highway Networks and Residual Nets as special cases. Experiments on large sequence and vector datasets demonstrate that the proposed gating scheme helps improve the learning speed significantly without extra overhead.

We develop a framework for warm-starting Bayesian optimization, that reduces the solution time required to solve an optimization problem that is one in a sequence of related problems. This is useful when optimizing the output of a stochastic simulator that fails to provide derivative information, for which Bayesian optimization methods are well-suited. Solving sequences of related optimization problems arises when making several business decisions using one optimization model and input data collected over different time periods or markets. While many gradient-based methods can be warm started by initiating optimization at the solution to the previous problem, this warm start approach does not apply to Bayesian optimization methods, which carry a full metamodel of the objective function from iteration to iteration. Our approach builds a joint statistical model of the entire collection of related objective functions, and uses a value of information calculation to recommend points to evaluate.

Use of computational methods to predict gene regulatory networks (GRNs) from gene expression data is a challenging task. Many studies have been conducted using unsupervised methods to fulfill the task; however, such methods usually yield low prediction accuracies due to the lack of training data. In this article, we propose semi-supervised methods for GRN prediction by utilizing two machine learning algorithms, namely support vector machines (SVM) and random forests (RF). The semi-supervised methods make use of unlabeled data for training. We investigate inductive and transductive learning approaches, both of which adopt an iterative procedure to obtain reliable negative training data from the unlabeled data. We then apply our semi-supervised methods to gene expression data of Escherichia coli and Saccharomyces cerevisiae, and evaluate the performance of our methods using the expression data. Our analysis indicated that the transductive learning approach outperformed the inductive learning approach for both organisms. However, there was no conclusive difference identified in the performance of SVM and RF. Experimental results also showed that the proposed semi-supervised methods performed better than existing supervised methods for both organisms.

Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these methods typically only apply to conditionally-conjugate models. We present a new stochastic method for variational inference which exploits the geometry of the variational-parameter space and also yields simple closed-form updates even for non-conjugate models. We also give a convergence-rate analysis of our method and many other previous methods which exploit the geometry of the space. Our analysis generalizes existing convergence results for stochastic mirror-descent on non-convex objectives by using a more general class of divergence functions. Beyond giving a theoretical justification for a variety of recent methods, our experiments show that new algorithms derived in this framework lead to state of the art results on a variety of problems. Further, due to its generality, we expect that our theoretical analysis could also apply to other applications.

We present our solution to the job recommendation task for RecSys Challenge 2016. The main contribution of our work is to combine temporal learning with sequence modeling to capture complex user-item activity patterns to improve job recommendations. First, we propose a time-based ranking model applied to historical observations and a hybrid matrix factorization over time re-weighted interactions. Second, we exploit sequence properties in user-items activities and develop a RNN-based recommendation model. Our solution achieved 5$^{th}$ place in the challenge among more than 100 participants. Notably, the strong performance of our RNN approach shows a promising new direction in employing sequence modeling for recommendation systems.

Estimating mutual information from i.i.d. samples drawn from an unknown joint density function is a basic statistical problem of broad interest with multitudinous applications. The most popular estimator is one proposed by Kraskov and St\"ogbauer and Grassberger (KSG) in 2004, and is nonparametric and based on the distances of each sample to its $k^{\rm th}$ nearest neighboring sample, where $k$ is a fixed small integer. Despite its widespread use (part of scientific software packages), theoretical properties of this estimator have been largely unexplored. In this paper we demonstrate that the estimator is consistent and also identify an upper bound on the rate of convergence of the bias as a function of number of samples. We argue that the superior performance benefits of the KSG estimator stems from a curious "correlation boosting" effect and build on this intuition to modify the KSG estimator in novel ways to construct a superior estimator. As a byproduct of our investigations, we obtain nearly tight rates of convergence of the $\ell_2$ error of the well known fixed $k$ nearest neighbor estimator of differential entropy by Kozachenko and Leonenko.