Estimating symmetric properties of a distribution, e.g. support size, coverage, entropy, distance to uniformity, are among the most fundamental problems in algorithmic statistics. While each of these properties have been studied extensively and separate optimal estimators are known for each, in striking recent work, Acharya et al. 2016 showed that there is a single estimator that is competitive for all symmetric properties. This work proved that computing the distribution that approximately maximizes \emph{profile likelihood (PML)}, i.e. the probability of observed frequency of frequencies, and returning the value of the property on this distribution is sample competitive with respect to a broad class of estimators of symmetric properties. Further, they showed that even computing an approximation of the PML suffices to achieve such a universal plug-in estimator. Unfortunately, prior to this work there was no known polynomial time algorithm to compute an approximate PML and it was open to obtain a polynomial time universal plug-in estimator through the use of approximate PML. In this paper we provide a algorithm (in number of samples) that, given $n$ samples from a distribution, computes an approximate PML distribution up to a multiplicative error of $\exp(n^{2/3} \mathrm{poly} \log(n))$ in time nearly linear in $n$. Generalizing work of Acharya et al. 2016 on the utility of approximate PML we show that our algorithm provides a nearly linear time universal plug-in estimator for all symmetric functions up to accuracy $\epsilon = \Omega(n^{-0.166})$. Further, we show how to extend our work to provide efficient polynomial-time algorithms for computing a $d$-dimensional generalization of PML (for constant $d$) that allows for universal plug-in estimation of symmetric relationships between distributions.

The network reconstruction problem is one of the challenging problems in network science. This work deals with reconstructing networks in which the flows are conserved around the nodes. These networks are referred to as conserved networks. We propose a novel concept of conservation graph for describing conserved networks. The properties of conservation graph are investigated. We develop a methodology to reconstruct conserved networks from flows by combining these graph properties with learning techniques, with polynomial time complexity. We show that exact network reconstruction is possible for radial networks. Further, we extend the methodology for reconstructing networks from noisy data. We demonstrate the proposed methods on different types of radial networks.

This paper proposes a geometric estimator of dependency between a pair of multivariate samples. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate samples. This estimator converges to a quantity that we call the geometric mutual information (GMI), which is equivalent to the Henze-Penrose divergence [1] between the joint distribution of the multivariate samples and the product of the marginals. The GMI has many of the same properties as standard MI but can be estimated from empirical data without density estimation; making it scalable to large datasets. The proposed empirical estimator of GMI is simple to implement, involving the construction of an MST spanning over both the original data and a randomly permuted version of this data. We establish asymptotic convergence of the estimator and convergence rates of the bias and variance for smooth multivariate density functions belonging to a H\"{o}lder class. We demonstrate the advantages of our proposed geometric dependency estimator in a series of experiments.

High sensitivity of neural architecture search (NAS) methods against their input such as step-size (i.e., learning rate) and search space prevents practitioners from applying them out-of-the-box to their own problems, albeit its purpose is to automate a part of tuning process. Aiming at a fast, robust, and widely-applicable NAS, we develop a generic optimization framework for NAS. We turn a coupled optimization of connection weights and neural architecture into a differentiable optimization by means of stochastic relaxation. It accepts arbitrary search space (widely-applicable) and enables to employ a gradient-based simultaneous optimization of weights and architecture (fast). We propose a stochastic natural gradient method with an adaptive step-size mechanism built upon our theoretical investigation (robust). Despite its simplicity and no problem-dependent parameter tuning, our method exhibited near state-of-the-art performances with low computational budgets both on image classification and inpainting tasks.

In this paper we use a time-evolving graph which consists of a sequence of graph snapshots over time to model many real-world networks. We study the path classification problem in a time-evolving graph, which has many applications in real-world scenarios, for example, predicting path failure in a telecommunication network and predicting path congestion in a traffic network in the near future. In order to capture the temporal dependency and graph structure dynamics, we design a novel deep neural network named Long Short-Term Memory R-GCN (LRGCN). LRGCN considers temporal dependency between time-adjacent graph snapshots as a special relation with memory, and uses relational GCN to jointly process both intra-time and inter-time relations. We also propose a new path representation method named self-attentive path embedding (SAPE), to embed paths of arbitrary length into fixed-length vectors. Through experiments on a real-world telecommunication network and a traffic network in California, we demonstrate the superiority of LRGCN to other competing methods in path failure prediction, and prove the effectiveness of SAPE on path representation.

Here, we study different update rules in stochastic gradient descent (SGD) for online forecasting problems. The selection of the learning rate parameter is critical in SGD. However, it may not be feasible to tune this parameter in online learning. Therefore, it is necessary to have an update rule that is not sensitive to the selection of the learning parameter. Inspired by the local regret metric that we introduced previously, we propose to use time-smoothed gradients within SGD update. Using the public data set-- GEFCom2014, we validate that our approach yields more stable results than the other existing approaches. Furthermore, we show that such a simple approach is computationally efficient compared to the alternatives.

Multiple machine learning and prediction models are often used for the same prediction or recommendation task. In our recent work, where we develop and deploy airline ancillary pricing models in an online setting, we found that among multiple pricing models developed, no one model clearly dominates other models for all incoming customer requests. Thus, as algorithm designers, we face an exploration - exploitation dilemma. In this work, we introduce an adaptive meta-decision framework that uses Thompson sampling, a popular multi-armed bandit solution method, to route customer requests to various pricing models based on their online performance. We show that this adaptive approach outperform a uniformly random selection policy by improving the expected revenue per offer by 43% and conversion score by 58% in an offline simulation.

There are different problems for resolution of complex LC-MS or GC-MS data, such as the existence of embedded chromatographic peaks, continuum background and overlapping in mass channels for different components. These problems cause rotational ambiguity in recovered profiles calculated using multivariate curve resolution (MCR) methods. Since mass spectra are sparse in nature, sparsity has been proposed recently as a constraint in MCR methods for analyzing LC-MS data. There are different ways for implementation of the sparsity constraint, and majority of methods rely on imposing a penalty based on the L0-, L1- and L2-norms of recovered mass spectra. Ridge regression and least absolute shrinkage and selection operator (Lasso) can be used for implementation of L2- and L1-norm penalties in MCR, respectively. The main question is which Lx-norm penalty is more worthwhile for implementation of the sparsity constraint in MCR methods. In order to address this question, two and three component LC-MS data were simulated and used for the case study in this work. The areas of feasible solutions (AFS) were calculated using the grid search strategy. Calculating Lx-norms values in AFS for x between zero and two revealed that the gradient of optimization surface increased from x values equal to two to x values near zero. However, for x equal to zero, the optimization surface was similar to a plateau, which increased the risk of sticking in local minima. Generally, results in this work, recommend the use of L1-norm penalty methods like Lasso for implementation of sparsity constraint in MCR-ALS algorithm for finding more sparse solutions and reducing the extent of rotational ambiguity.

Inverse reinforcement learning (IRL) is an ill-posed inverse problem since expert demonstrations may infer many solutions of reward functions which is hard to recover by local search methods such as a gradient method. In this paper, we generalize the original IRL problem to recover a probability distribution for reward functions. We call such a generalized problem stochastic inverse reinforcement learning (SIRL) which is first formulated as an expectation optimization problem. We adopt the Monte Carlo expectation-maximization (MCEM) method, a global search method, to estimate the parameter of the probability distribution as the first solution to SIRL. With our approach, it is possible to observe the deep intrinsic property in IRL from a global viewpoint, and the technique achieves a considerable robust recovery performance on the classic learning environment, objectworld.

Classical neural networks add a bias term to the sum of all weighted inputs. For capsule networks, the routing-by-agreement algorithm, which is commonly used to route vectors from lower level capsules to upper level capsules, calculates activations without a bias term. In this paper we show that such a term is also necessary for routing-by-agreement. We will proof that for every input there exists a symmetric input that cannot be distinguished correctly by capsules without a bias term. We show that this limitation impacts the training of deeper capsule networks negatively and that adding a bias term allows for the training of deeper capsule networks. An alternative to a bias is also presented in this paper. This novel method does not introduce additional parameters and is directly encoded in the activation vector of capsules.