Trip recommendation is an important location-based service that helps relieve users from the time and efforts for trip planning. It aims to recommend a sequence of places of interest (POIs) for a user to visit that maximizes the user's satisfaction. When adding a POI to a recommended trip, it is essential to understand the context of the recommendation, including the POI popularity, other POIs co-occurring in the trip, and the preferences of the user. These contextual factors are learned separately in existing studies, while in reality, they impact jointly on a user's choice of a POI to visit. In this study, we propose a POI embedding model to jointly learn the impact of these contextual factors. We call the learned POI embedding a context-aware POI embedding. To showcase the effectiveness of this embedding, we apply it to generate trip recommendations given a user and a time budget. We propose two trip recommendation algorithms based on our context-aware POI embedding. The first algorithm finds the exact optimal trip by transforming and solving the trip recommendation problem as an integer linear programming problem. To achieve a high computation efficiency, the second algorithm finds a heuristically optimal trip based on adaptive large neighborhood search. We perform extensive experiments on real datasets. The results show that our proposed algorithms consistently outperform state-of-the-art algorithms in trip recommendation quality, with an advantage of up to 43% in F1-score.

We focus on solving the clustered lasso problem, which is a least squares problem with the $\ell_1$-type penalties imposed on both the coefficients and their pairwise differences to learn the group structure of the regression parameters. Here we first reformulate the clustered lasso regularizer as a weighted ordered-lasso regularizer, which is essential in reducing the computational cost from $O(n^2)$ to $O(n\log (n))$. We then propose an inexact semismooth Newton augmented Lagrangian (SSNAL) algorithm to solve the clustered lasso problem or its dual via this equivalent formulation, depending on whether the sample size is larger than the dimension of the features. An essential component of the SSNAL algorithm is the computation of the generalized Jacobian of the proximal mapping of the clustered lasso regularizer. Based on the new formulation, we derive an efficient procedure for its computation. Comprehensive results on the global convergence and local linear convergence of the SSNAL algorithm are established. For the purpose of exposition and comparison, we also summarize/design several first-order methods that can be used to solve the problem under consideration, but with the key improvement from the new formulation of the clustered lasso regularizer. As a demonstration of the applicability of our algorithms, numerical experiments on the clustered lasso problem are performed. The experiments show that the SSNAL algorithm substantially outperforms the best alternative algorithm for the clustered lasso problem.

State-of-the-art distributed machine learning suffers from significant delays due to frequent communication and synchronizing between worker nodes. Emerging communication-efficient SGD algorithms that limit synchronization between locally trained models have been shown to be effective in speeding-up distributed SGD. However, a rigorous convergence analysis and comparative study of different communication-reduction strategies remains a largely open problem. This paper presents a new framework called Coooperative SGD that subsumes existing communication-efficient SGD algorithms such as federated-averaging, elastic-averaging and decentralized SGD. By analyzing Cooperative SGD, we provide novel convergence guarantees for existing algorithms. Moreover this framework enables us to design new communication-efficient SGD algorithms that strike the best balance between reducing communication overhead and achieving fast error convergence.

Information bottleneck (IB) is a method for extracting information from one random variable X that is relevant for predicting another random variable Y . To do so, IB identifies an intermediate "bottleneck" variable T that has low mutual information I(X; T) and high mutual information I(Y; T). The IB curve characterizes the set of bottleneck variables that achieve maximal I(Y; T) for a given I(X; T), and is typically explored by optimizing the IB Lagrangian, I(Y; T) βI(X; T). Recently, there has been interest in applying IB to supervised learning, particularly for classification problems that use neural networks. In most classification problems, the output class Y is a deterministic function of the input X, which we refer to as "deterministic supervised learning". We demonstrate three pathologies that arise when IB is used in any scenario where Y is a deterministic function of X: (1) the IB curve cannot be recovered by optimizing the IB Lagrangian for different values of β; (2) there are "uninteresting" solutions at all points of the IB curve; and (3) for classifiers that achieve low error rates, the activity of different hidden layers will not exhibit a strict tradeoff between compression and prediction, contrary to a recent proposal. To address problem (1), we propose a functional that, unlike the IB Lagrangian, can recover the IB curve in all cases. We finish by demonstrating these issues on the MNIST dataset. The information bottleneck (IB) method (Tishby et al., 1999) provides a principled way to extract information that is present in one variable that is relevant for predicting another variable. Given two random variables X and Y, IB posits a "bottleneck" variable T that obeys the Markov condition Y X T . By the data processing inequality (DPI) (Cover & Thomas, 2012), this Markov condition implies that I(X; T) I(Y; T), meaning the bottleneck variable cannot contain more information about Y than it does about X.

Bayesian optimization (BO) is a popular algorithm for solving challenging optimization tasks. It is designed for problems where the objective function is expensive to evaluate, perhaps not available in exact form, without gradient information and possibly returning noisy values. Different versions of the algorithm vary in the choice of the acquisition function, which recommends the point to query the objective at next. Initially, researchers focused on improvement-based acquisitions, while recently the attention has shifted to more computationally expensive information-theoretical measures. In this paper we present two major contributions to the literature. First, we propose a new improvement-based acquisition function that recommends query points where the improvement is expected to be high with high confidence. The proposed algorithm is evaluated on a large set of benchmark functions from the global optimization literature, where it turns out to perform at least as well as current state-of-the-art acquisition functions, and often better. This suggests that it is a powerful default choice for BO. The novel policy is then compared to widely used global optimization solvers in order to confirm that BO methods reduce the computational costs of the optimization by keeping the number of function evaluations small. The second main contribution represents an application to precision medicine, where the interest lies in the estimation of parameters of a partial differential equations model of the human pulmonary blood circulation system. Once inferred, these parameters can help clinicians in diagnosing a patient with pulmonary hypertension without going through the standard invasive procedure of right heart catheterization, which can lead to side effects and complications (e.g. severe pain, internal bleeding, thrombosis).

Research and Services Division of Materials Data and Integrated System, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan We present a novel optimization method, named the Combined Optimization Method (COM), for the joint optimization of two or more cost functions. Unlike the conventional joint optimization schemes, which try to find minima in a weighted sum of cost functions, the COM explores search space for common minima shared by all the cost functions. Given a set of multiple cost functions that have qualitatively different distributions of local minima with each other, the proposed method finds the common minima with a high success rate without the help of any metaheuristics. As a demonstration, we apply the COM to the crystal structure prediction in materials science. By introducing the concept of data assimilation, i.e., adopting the theoretical potential energy of the crystal and the crystallinity, which characterizes the agreement with the theoretical and experimental X-ray diffraction patterns, as cost functions, we show that the correct crystal structures of Si diamond, low quartz, and low cristobalite can be predicted with significantly higher success rates than the previous methods. Continuous optimization, i.e., finding a global minimum of a continuous nonlinear cost function, is one of the most fundamental and important problems encountered in almost all the fields of science and engineering. For solving the optimization problem, a variety of classical optimization algorithms, such as the gradient descent, conjugate gradient, Newton and quasi-Newton methods, downhill simplex method, etc. have been developed so far and long been used widely [1]. If the cost function has a rugged landscape in a high-dimensional search space, however, such classical algorithms easily fail to find the global optimal point, and get trapped by local minima, or metastable states.

Real-world data sets often provide multiple types of information about the same set of entities. This data is well represented by multi-view graphs, which consist of several distinct sets of edges over the same nodes. These can be used to analyze how entities interact from different viewpoints. Combining multiple views improves the quality of inferences drawn from the underlying data, which has increased interest in developing efficient multi-view graph embedding methods. We propose an algorithm, C-RSP, that generates a common (C) embedding of a multi-view graph using Randomized Shortest Paths (RSP). This algorithm generates a dissimilarity measure between nodes by minimizing the expected cost of a random walk between any two nodes across all views of a multi-view graph, in doing so encoding both the local and global structure of the graph. We test C-RSP on both real and synthetic data and show that it outperforms benchmark algorithms at embedding and clustering tasks while remaining computationally efficient.

Recently, network lasso has drawn many attentions due to its remarkable performance on simultaneous clustering and optimization. However, it usually suffers from the imperfect data (noise, missing values etc), and yields sub-optimal solutions. The reason is that it finds the similar instances according to their features directly, which is usually impacted by the imperfect data, and thus returns sub-optimal results. In this paper, we propose triangle lasso to avoid its disadvantage. Triangle lasso finds the similar instances according to their neighbours. If two instances have many common neighbours, they tend to become similar. Although some instances are profiled by the imperfect data, it is still able to find the similar counterparts. Furthermore, we develop an efficient algorithm based on Alternating Direction Method of Multipliers (ADMM) to obtain a moderately accurate solution. In addition, we present a dual method to obtain the accurate solution with the low additional time consumption. We demonstrate through extensive numerical experiments that triangle lasso is robust to the imperfect data. It usually yields a better performance than the state-of-the-art method when performing data analysis tasks in practical scenarios.

In the past decade, sparse and low-rank recovery have drawn much attention in many areas such as signal/image processing, statistics, bioinformatics and machine learning. To achieve sparsity and/or low-rankness inducing, the $\ell_1$ norm and nuclear norm are of the most popular regularization penalties due to their convexity. While the $\ell_1$ and nuclear norm are convenient as the related convex optimization problems are usually tractable, it has been shown in many applications that a nonconvex penalty can yield significantly better performance. In recent, nonconvex regularization based sparse and low-rank recovery is of considerable interest and it in fact is a main driver of the recent progress in nonconvex and nonsmooth optimization. This paper gives an overview of this topic in various fields in signal processing, statistics and machine learning, including compressive sensing (CS), sparse regression and variable selection, sparse signals separation, sparse principal component analysis (PCA), large covariance and inverse covariance matrices estimation, matrix completion, and robust PCA. We present recent developments of nonconvex regularization based sparse and low-rank recovery in these fields, addressing the issues of penalty selection, applications and the convergence of nonconvex algorithms.

AutoML serves as the bridge between varying levels of expertise when designing machine learning systems and expedites the data science process. A wide range of techniques is taken to address this, however there does not exist an objective comparison of these techniques. We present a benchmark of current open source AutoML solutions using open source datasets. We test auto-sklearn, TPOT, auto_ml, and H2O's AutoML solution against a compiled set of regression and classification datasets sourced from OpenML and find that auto-sklearn performs the best across classification datasets and TPOT performs the best across regression datasets.