We propose a K-sparse exhaustive search (ES-K) method and a K-sparse approximate exhaustive search method (AES-K) for selecting variables in linear regression. With these methods, K-sparse combinations of variables are tested exhaustively assuming that the optimal combination of explanatory variables is K-sparse. By collecting the results of exhaustively computing ES-K, various approximate methods for selecting sparse variables can be summarized as density of states. With this density of states, we can compare different methods for selecting sparse variables such as relaxation and sampling. For large problems where the combinatorial explosion of explanatory variables is crucial, the AES-K method enables density of states to be effectively reconstructed by using the replica-exchange Monte Carlo method and the multiple histogram method. Applying the ES-K and AES-K methods to type Ia supernova data, we confirmed the conventional understanding in astronomy when an appropriate K is given beforehand. However, we found the difficulty to determine K from the data. Using virtual measurement and analysis, we argue that this is caused by data shortage.

It was because of the letter K that I found my youn ger sister, but for 14 years, it was also the letter K that kept us apart. I'd been searching for her online under variations of the name Maria Christina Sugatan since we lost touch in 1997, after our mom refused to let me speak to her. She was Maria at school but Chris at home and, later, Chrissy. It became my ritual to search for variations of her name online. Meredith Talusan is a freelance writer focusing on minority issues.

Automation and computer intelligence to support complex human decisions becomes essential to manage large and distributed systems in the Cloud and IoT era. Understanding the root cause of an observed symptom in a complex system has been a major problem for decades. As industry dives into the IoT world and the amount of data generated per year grows at an amazing speed, an important question is how to find appropriate mechanisms to determine root causes that can handle huge amounts of data or may provide valuable feedback in real-time. While many survey papers aim at summarizing the landscape of techniques for modelling system behavior and infering the root cause of a problem based in the resulting models, none of those focuses on analyzing how the different techniques in the literature fit growing requirements in terms of performance and scalability. In this survey, we provide a review of root-cause analysis, focusing on these particular aspects. We also provide guidance to choose the best root-cause analysis strategy depending on the requirements of a particular system and application.

If you thought solving a Rubik's cube was difficult, you were right and maths can back you up. A recent study shows that the question of whether a scrambled Rubik's cube of any size can be solved in a given number of moves is what's called NP-complete – that's maths lingo for a problem even mathematicians find hard to solve. To prove that the problem is NP-complete, Massachusetts Institute of Technology researchers Erik Demaine, Sarah Eisenstat, and Mikhail Rudoy showed that figuring out how to solve a Rubik's cube with any number of squares on a side in the smallest number of moves will also give you a solution to another problem known to be NP-complete: the Hamiltonian path problem. That question asks whether there is route that visits each vertex exactly once in a given graph consisting of a collection of vertices connected by edges, like a triangle, pentagram, or the vast connections in a social network such as Facebook. It's reminiscent of the travelling salesperson problem, which aims to find the shortest route that visits several cities only once, probably the most famous NP-complete question of all.

We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we consider goodness-of-fit testing when the null distribution has a possibly growing or unbounded number of categories. In the continuous case, we consider testing a Lipschitz density, with possibly unbounded support, in the low-smoothness regime where the Lipschitz parameter is not assumed to be constant. In contrast to existing results, we show that the minimax rate and critical testing radius in these settings depend strongly, and in a precise way, on the null distribution being tested and this motivates the study of the (local) minimax rate as a function of the null distribution. For multinomials the local minimax rate was recently studied in the work of Valiant and Valiant. We re-visit and extend their results and develop two modifications to the chi-squared test whose performance we characterize. For testing Lipschitz densities, we show that the usual binning tests are inadequate in the low-smoothness regime and we design a spatially adaptive partitioning scheme that forms the basis for our locally minimax optimal tests. Furthermore, we provide the first local minimax lower bounds for this problem which yield a sharp characterization of the dependence of the critical radius on the null hypothesis being tested. In the low-smoothness regime we also provide adaptive tests, that adapt to the unknown smoothness parameter. We illustrate our results with a variety of simulations that demonstrate the practical utility of our proposed tests.

The paper deals with the adaptation of a new measure for the unsupervised feature selection problems. The proposed measure is based on space filling concept and is called the coverage measure. This measure was used for judging the quality of an experimental space filling design. In the present work, the coverage measure is adapted for selecting the smallest informative subset of variables by reducing redundancy in data. This paper proposes a simple analogy to apply this measure. It is implemented in a filter algorithm for unsupervised feature selection problems. The proposed filter algorithm is robust with high dimensional data and can be implemented without extra parameters. Further, it is tested with simulated data and real world case studies including environmental data and hyperspectral image. Finally, the results are evaluated by using random forest algorithm.

Using these libraries will help us focus only on the most interesting task: creating the algorithm that finds the best move. We'll start by creating a function that just returns a random move from all of the possible moves: Although this algorithm isn't a very solid chess player, it's a good starting point, as we can actually play against it: Now let's try to understand which side is stronger in a certain position. With the evaluation function, we're able to create an algorithm that chooses the move that gives the highest evaluation: The only tangible improvement is that our algorithm will now capture a piece if it can. Next we're going to create a search tree from which the algorithm can chose the best move. This is done by using the Minimax algorithm.

An instance of the n-puzzle game consists of a board holding n 2-1 distinct movable tiles, plus an empty space. The tiles are numbers from the set 1,..,n 2-1. For any such board, the empty space may be legally swapped with any tile horizontally or vertically adjacent to it. In this assignment, the blank space is going to be represented with the number 0. Given an initial state of the board, the combinatorial search problem is to find a sequence of moves that transitions this state to the goal state; that is, the configuration with all tiles arranged in ascending order 0,1,…,n 2 1. The search space is the set of all possible states reachable from the initial state.

Today, Businesses Have More Ways – And Places – Than Ever To Market Themselves.Your Local Digital Marketing Strategy Should Specifically Target And Appeal To Potential Customers In Your Geographic Area. Many Local Companies Have Used Some Form Of Digital Marketing Online Even If They Are Not Aware Of It.This Is An Important Local Digital Marketing Tip For Any Business. But For Local Businesses, It Can Be Even More Essential. Customers Who Are Looking For A Restaurant, Store Or Other Local Business Are Likely To Do A Search On Their Phone Or Mobile Device. If You Don't Have A Mobile Optimized Site, Not Only Will It Be Difficult For Them To Interact With Your Site, But It Will Also Be Difficult For Them To Find It In The First Place. If You Want Local Customers, Either On Mobile Or Desktop, To Find You, You Have To Have A Comprehensive Search Strategy.

We adopt data structure in the form of cover trees and iteratively apply approximate nearest neighbour (ANN) searches for fast compressed sensing reconstruction of signals living on discrete smooth manifolds. Levering on the recent stability results for the inexact Iterative Projected Gradient (IPG) algorithm and by using the cover tree's ANN searches, we decrease the projection cost of the IPG algorithm to be logarithmically growing with data population for low dimensional smooth manifolds. We apply our results to quantitative MRI compressed sensing and in particular within the Magnetic Resonance Fingerprinting (MRF) framework. For a similar (or sometimes better) reconstruction accuracy, we report 2-3 orders of magnitude reduction in computations compared to the standard iterative method which uses brute-force searches.