The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ($\Phi$) in the brain is related to the level of consciousness. IIT proposes that to quantify information integration in a system as a whole, integrated information should be measured across the partition of the system at which information loss caused by partitioning is minimized, called the Minimum Information Partition (MIP). The computational cost for exhaustively searching for the MIP grows exponentially with system size, making it difficult to apply IIT to real neural data. It has been previously shown that if a measure of $\Phi$ satisfies a mathematical property, submodularity, the MIP can be found in a polynomial order by an optimization algorithm. However, although the first version of $\Phi$ is submodular, the later versions are not. In this study, we empirically explore to what extent the algorithm can be applied to the non-submodular measures of $\Phi$ by evaluating the accuracy of the algorithm in simulated data and real neural data. We find that the algorithm identifies the MIP in a nearly perfect manner even for the non-submodular measures. Our results show that the algorithm allows us to measure $\Phi$ in large systems within a practical amount of time.

A parametric point process model is developed, with modeling based on the assumption that sequential observations often share latent phenomena, while also possessing idiosyncratic effects. An alternating optimization method is proposed to learn a "registered" point process that accounts for shared structure, as well as "warping" functions that characterize idiosyncratic aspects of each observed sequence. Under reasonable constraints, in each iteration we update the sample-specific warping functions by solving a set of constrained nonlinear programming problems in parallel, and update the model by maximum likelihood estimation. The justifiability, complexity and robustness of the proposed method are investigated in detail, and the influence of sequence stitching on the learning results is examined empirically. Experiments on both synthetic and real-world data demonstrate that the method yields explainable point process models, achieving encouraging results compared to state-of-the-art methods.

Driven by the need for parallelizable hyperparameter optimization methods, this paper studies \emph{open loop} search methods: sequences that are predetermined and can be generated before a single configuration is evaluated. Examples include grid search, uniform random search, low discrepancy sequences, and other sampling distributions. In particular, we propose the use of $k$-determinantal point processes in hyperparameter optimization via random search. Compared to conventional uniform random search where hyperparameter settings are sampled independently, a $k$-DPP promotes diversity. We describe an approach that transforms hyperparameter search spaces for efficient use with a $k$-DPP. In addition, we introduce a novel Metropolis-Hastings algorithm which can sample from $k$-DPPs defined over any space from which uniform samples can be drawn, including spaces with a mixture of discrete and continuous dimensions or tree structure. Our experiments show significant benefits in realistic scenarios with a limited budget for training supervised learners, whether in serial or parallel.

We present NeuroSAT, a message passing neural network that learns to solve SAT problems after only being trained as a classifier to predict satisfiability. Although it is not competitive with state-of-the-art SAT solvers, NeuroSAT can solve problems that are substantially larger and more difficult than it ever saw during training by simply running for more iterations. Moreover, NeuroSAT generalizes to novel distributions; after training only on random SAT problems, at test time it can solve SAT problems encoding graph coloring, clique detection, dominating set, and vertex cover problems, all on a range of distributions over small random graphs.

Dial-A-Ride Problem (DARP) addresses the issue of doorto-door transportation service for the customers with high customer satisfaction. Now-a-days, transportation services have increasing need in our daily life, and it started to directly impact our environment as well as quality of living. According to a study conducted by University of British Columbia, the road pricing or pay-per-use is the most effective way to reduce emissions and traffic [1]. DARP has many applications ranging from taxi services to autonomous cargo and ground operations at the airports. DARP is an extension of pickup and delivery problem under the class of vehicle routing problem (VRP) [2]. It is a combinatorial optimization problem with an objective function to minimise the overall cost while satisfying a specific set of constraints such as time-window, maximum waiting time and maximum ride time to ensure high-quality customer service. In this problem, a set of customers makes a request for pickup and drop-off at certain locations within a predefined time-window. An approach to solve DARP based on dynamic programming has been proposed in [3], in which divide and conquer method is used to solve the problem.

We introduce SCAL, an algorithm designed to perform efficient exploration-exploitation in any unknown weakly-communicating Markov Decision Process (MDP) for which an upper bound c on the span of the optimal bias function is known. For an MDP with S states, A actions and Gamma <= S possible next states, we prove a regret bound of O(c\sqrt{Gamma SAT}), which significantly improves over existing algorithms (e.g., UCRL and PSRL), whose regret scales linearly with the MDP diameter D. In fact, the optimal bias span is finite and often much smaller than D (e.g., D=infinity in non-communicating MDPs). A similar result was originally derived by Bartlett and Tewari (2009) for REGAL.C, for which no tractable algorithm is available. In this paper, we relax the optimization problem at the core of REGAL.C, we carefully analyze its properties, and we provide the first computationally efficient algorithm to solve it. Finally, we report numerical simulations supporting our theoretical findings and showing how SCAL significantly outperforms UCRL in MDPs with large diameter and small span.

Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or regularized variations such as Sinkhorn distance. However, as we will demonstrate, several important machine learning applications call for the computation of exact Wasserstein distance, and regularized variations with small regularization parameter will fail due to numerical stability issues or degradate the performance. We address this challenge by developing an Inexact Proximal point method for Optimal Transport (IPOT) with the proximal operator approximately evaluated at each iteration using projections to the probability simplex. We also simplify the architecture for learning generative models based on optimal transport solution, and generalize the idea of IPOT to a new method for computing Wasserstein barycenter. We provide convergence analysis of IPOT and experiments showing our new methods outperform the state-of-the-art methods in terms of both effectiveness and efficiency.

We present an end-to-end framework for solving Vehicle Routing Problem (VRP) using deep reinforcement learning. In this approach, we train a single model that finds near-optimal solutions for problem instances sampled from a given distribution, only by observing the reward signals and following feasibility rules. Our model represents a parameterized stochastic policy, and by applying a policy gradient algorithm to optimize its parameters, the trained model produces the solution as a sequence of consecutive actions in real time, without the need to re-train for every new problem instance. Our method is faster in both training and inference than a recent method that solves the Traveling Salesman Problem (TSP), with nearly identical solution quality. On the more general VRP, our approach outperforms classical heuristics on medium-sized instances in both solution quality and computation time (after training). Our proposed framework can be applied to variants of the VRP such as the stochastic VRP, and has the potential to be applied more generally to combinatorial optimization problems.

We study safe screening for metric learning. Distance metric learning can optimize a metric over a set of triplets, each one of which is defined by a pair of same class instances and an instance in a different class. However, the number of possible triplets is quite huge even for a small dataset. Our safe triplet screening identifies triplets which can be safely removed from the optimization problem without losing the optimality. Compared with existing safe screening studies, triplet screening is particularly significant because of (1) the huge number of possible triplets, and (2) the semi-definite constraint in the optimization. We derive several variants of screening rules, and analyze their relationships. Numerical experiments on benchmark datasets demonstrate the effectiveness of safe triplet screening.

We further assume that the space X is continuous. Such optimization problems are common in scientific and engineering fields. Examples include learning continuous valuation models (Eric, Freitas and Ghosh, 2008), automatic gait optimization for both quadrupedal and bipedal robots (Lizotte et al., 2007), choosing the optimal derivative of a molecule that best treats a disease (Negoescu, Frazier and Powell, 2011), tuning Hamiltonian based Monte Carlo Samplers (Wang, Mohamed and de Freitas, 2013), etc. A good survey of the problem in practical machine learning applications is presented in Snoek, Larochelle and Adams (2012). We were motivated to study this problem with the application of ranking multiple items on a webpage so as to optimize a diverse range of business metrics like user engagement and revenue from advertisements. In our example, the function f(x) is a utility function composed of various business metrics and x are parameters or knobs that control the relative frequency of different types of items we show on the webpage.