In this research, we investigate the subject of path-finding. A pruned version of visibility graph based on Candidate Vertices is formulated, followed by a new visibility check technique. Such combination enables us to quickly identify the useful vertices and thus find the optimal path more efficiently. The algorithm proposed is demonstrated on various path-finding cases. The performance of the new technique on visibility graphs is compared to the traditional A* on Grids, Theta* and A* on Visibility Graphs in terms of path length, number of nodes evaluated, as well as computational time. The key algorithmic contribution is that the new approach combines the merits of grid-based method and visibility graph-based method and thus yields better overall performance.

Analyzing time series data is important to predict future events and changes in finance, manufacturing, and administrative decisions. Gaussian processes (GPs) solve regression and classification problems by choosing appropriate kernels capturing covariance structure of data. In time series analysis, GP based regression methods recently demonstrate competitive performance by decomposing temporal covariance structure. Such covariance structure decomposition allows exploiting shared parameters over a set of multiple but selected time series. In this paper, we handle multiple time series by placing an Indian Buffet Process (IBP) prior on the presence of shared kernels. We investigate the validity of model when infinite latent components are introduced. We also propose an improved search algorithm to find interpretable kernels among multiple time series along with comparison reports. Experiments are conducted on both synthetic data sets and real world data sets, showing promising results in term of structure discoveries and predictive performances.

In this paper, we consider regression problems with one-hidden-layer neural networks (1NNs). We distill some properties of activation functions that lead to $\mathit{local~strong~convexity}$ in the neighborhood of the ground-truth parameters for the 1NN squared-loss objective. Most popular nonlinear activation functions satisfy the distilled properties, including rectified linear units (ReLUs), leaky ReLUs, squared ReLUs and sigmoids. For activation functions that are also smooth, we show $\mathit{local~linear~convergence}$ guarantees of gradient descent under a resampling rule. For homogeneous activations, we show tensor methods are able to initialize the parameters to fall into the local strong convexity region. As a result, tensor initialization followed by gradient descent is guaranteed to recover the ground truth with sample complexity $ d \cdot \log(1/\epsilon) \cdot \mathrm{poly}(k,\lambda )$ and computational complexity $n\cdot d \cdot \mathrm{poly}(k,\lambda) $ for smooth homogeneous activations with high probability, where $d$ is the dimension of the input, $k$ ($k\leq d$) is the number of hidden nodes, $\lambda$ is a conditioning property of the ground-truth parameter matrix between the input layer and the hidden layer, $\epsilon$ is the targeted precision and $n$ is the number of samples. To the best of our knowledge, this is the first work that provides recovery guarantees for 1NNs with both sample complexity and computational complexity $\mathit{linear}$ in the input dimension and $\mathit{logarithmic}$ in the precision.

A learning rule is an algorithm or mathematical expression that specifies precisely how the parameters should be changed. When creating an artificial intelligence system, we must make two decisions: what representation should be used (i.e., what parameterized function should be used) and what learning rule should be used to search through the resulting set of representable functions. Using most learning rules, these two decisions are coupled in a subtle (and often unintentional) way. That is, using the same learning rule with two different representations that can represent the same sets of functions can result in two different outcomes. After arguing that this coupling is undesirable, particularly when using artificial neural networks, we present a method for partially decoupling these two decisions for a broad class of learning rules that span unsupervised learning, reinforcement learning, and supervised learning.

Reinforcement Learning (RL) is the task of training an agent to perform optimally in an environment using the reward and observation signals perceived upon taking actions which change the environment dynamics. Learning optimal behavior is inherently difficult because of challenges like credit assignment and exploration-exploitation trade offs that need to be made while converging to a solution. In many scenarios, like training a rover to move on a Martian surface, the cost of obtaining samples for learning can be high (in terms of robot's energy expenditure etc.), and so sample efficiency is an important subproblem which deserves special attention. Very often it is the case that the environment has intrinsic symmetries which can be leveraged by the agent to improve performance and learn more efficiently. For example, in the Cart-Pole domain [1, 2] the state action space is symmetric with respect to reflection about the plane perpendicular to the direction of motion of the cart (Figure 1). In fact, in many environments, the number of symmetry relations tend to increase with the dimensionality of the state space. For instance, for the simple case of grid world of dimension d (Figure 1) there exist O(d!2

In retailer management, the Newsvendor problem has widely attracted attention as one of basic inventory models. In the traditional approach to solving this problem, it relies on the probability distribution of the demand. In theory, if the probability distribution is known, the problem can be considered as fully solved. However, in any real world scenario, it is almost impossible to even approximate or estimate a better probability distribution for the demand. In recent years, researchers start adopting machine learning approach to learn a demand prediction model by using other feature information. In this paper, we propose a supervised learning that optimizes the demand quantities for products based on feature information. We demonstrate that the original Newsvendor loss function as the training objective outperforms the recently suggested quadratic loss function. The new algorithm has been assessed on both the synthetic data and real-world data, demonstrating better performance.

We present a solution to scale spectral algorithms for learning sequence functions. We are interested in the case where these functions are sparse (that is, for most sequences they return 0). Spectral algorithms reduce the learning problem to the task of computing an SVD decomposition over a special type of matrix called the Hankel matrix. This matrix is designed to capture the relevant statistics of the training sequences. What is crucial is that to capture long range dependencies we must consider very large Hankel matrices. Thus the computation of the SVD becomes a critical bottleneck. Our solution finds a subset of rows and columns of the Hankel that realizes a compact and informative Hankel submatrix. The novelty lies in the way that this subset is selected: we exploit a maximal bipartite matching combinatorial algorithm to look for a sub-block with full structural rank, and show how computation of this sub-block can be further improved by exploiting the specific structure of Hankel matrices.

We introduce a generic scheme to solve nonconvex optimization problems using gradient-based algorithms originally designed for minimizing convex functions. When the objective is convex, the proposed approach enjoys the same properties as the Catalyst approach of Lin et al. [22]. When the objective is nonconvex, it achieves the best known convergence rate to stationary points for first-order methods. Specifically, the proposed algorithm does not require knowledge about the convexity of the objective; yet, it obtains an overall worst-case efficiency of $\tilde{O}(\varepsilon^{-2})$ and, if the function is convex, the complexity reduces to the near-optimal rate $\tilde{O}(\varepsilon^{-2/3})$. We conclude the paper by showing promising experimental results obtained by applying the proposed approach to SVRG and SAGA for sparse matrix factorization and for learning neural networks.

Deep neural networks have been shown to be very successful at learning feature hierarchies in supervised learning tasks. Generative models, on the other hand, have benefited less from hierarchical models with multiple layers of latent variables. In this paper, we prove that hierarchical latent variable models do not take advantage of the hierarchical structure when trained with existing variational methods, and provide some limitations on the kind of features existing models can learn. Finally we propose an alternative architecture that do not suffer from these limitations. Our model is able to learn highly interpretable and disentangled hierarchical features on several natural image datasets with no task specific regularization or prior knowledge.

Nonlinear kernel regression models are often used in statistics and machine learning because they are more accurate than linear models. Variable selection for kernel regression models is a challenge partly because, unlike the linear regression setting, there is no clear concept of an effect size for regression coefficients. In this paper, we propose a novel framework that provides an effect size analog of each explanatory variable for Bayesian kernel regression models when the kernel is shift-invariant --- for example, the Gaussian kernel. We use function analytic properties of shift-invariant reproducing kernel Hilbert spaces (RKHS) to define a linear vector space that: (i) captures nonlinear structure, and (ii) can be projected onto the original explanatory variables. The projection onto the original explanatory variables serves as an analog of effect sizes. The specific function analytic property we use is that shift-invariant kernel functions can be approximated via random Fourier bases. Based on the random Fourier expansion we propose a computationally efficient class of Bayesian approximate kernel regression (BAKR) models for both nonlinear regression and binary classification for which one can compute an analog of effect sizes. We illustrate the utility of BAKR by examining two important problems in statistical genetics: genomic selection (i.e. phenotypic prediction) and association mapping (i.e. inference of significant variants or loci). State-of-the-art methods for genomic selection and association mapping are based on kernel regression and linear models, respectively. BAKR is the first method that is competitive in both settings.