A Graph is a data structure consisting of finite number of nodes (or vertices) and edges that connect them. The numbered circles are nodes with the lines connecting them being the edges. A pair (0,1) represents an edge that connects the nodes or vertices 0 and 1. Graphs are used to represent and solve many real life problems. For example, they can represent any network which could be social media like Facebook, LinkedIn etc. or Google maps. In graph search, we traverse or search the graph data structure from node to node. The easiest to understand example would be that of navigation maps like Google Maps.

Quantum computing is a promising new paradigm for computer science. Quantum algorithms have proven themselves superior to classical ones in some classes of problems. The major examples are Shor's algorithm for solving the hidden subgroup problem and Grover's algorithm for the unstructured search problem, but quantum computing is not limited to them[18]. Simulating complex atomic systems using a quantum computer[8] could profoundly impact physics research since a quantum computer can naturally simulate the effects of quantum mechanics. Quantum Computing has also been impactful in the machine learning field. Basic linear algebra subroutines, such as Fourier transform, finding eigenvectors and eigenvalues, and solving linear equations, for example, exhibit exponential quantum speedups over their best known classical counterparts[4] Also, quantum machine learning aims to implement machine learning algorithms in quantum systems, by using the quantum properties such as superposition and entanglement to solve these problems efficiently[17]. However, practical limitations still hinder the development of a universal quantum computer that could use such algorithms. Current quantum computers are referred to as NISQ (Noisy Intermediate-Scale Quantum) computers [22] because of qubits imperfections and their available limited number, currently between 50 and 100. These numbers are not sufficient to execute error-correcting codes once 9 qubits are necessary to make 1 qubit fault-tolerant [7].

Artificial intelligence (AI) is becoming increasingly more popular and can be found in workplaces and homes around the world. However, how do we ensure trust in these systems? Regulation changes such as the GDPR mean that users have a right to understand how their data has been processed as well as saved. Therefore if, for example, you are denied a loan you have the right to ask why. This can be hard if the method for working this out uses "black box" machine learning techniques such as neural networks. TrustyAI is a new initiative which looks into explainable artificial intelligence (XAI) solutions to address trustworthiness in ML as well as decision services landscapes. In this paper we will look at how TrustyAI can support trust in decision services and predictive models. We investigate techniques such as LIME, SHAP and counterfactuals, benchmarking both LIME and counterfactual techniques against existing implementations. We also look into an extended version of SHAP, which supports background data selection to be evaluated based on quantitative data and allows for error bounds.

This paper presents and evaluates two pruning techniques to reinforce the efficiency of constraint optimization solvers based on multi-valued decision-diagrams (MDD). It adopts the branch-and-bound framework proposed by Bergman et al. in 2016 to solve dynamic programs to optimality. In particular, our paper presents and evaluates the effectiveness of the local-bound (LocB) and rough upper-bound pruning (RUB). LocB is a new and effective rule that leverages the approximate MDD structure to avoid the exploration of non-interesting nodes. RUB is a rule to reduce the search space during the development of bounded-width-MDDs. The experimental study we conducted on the Maximum Independent Set Problem (MISP), Maximum Cut Problem (MCP), Maximum 2 Satisfiability (MAX2SAT) and the Traveling Salesman Problem with Time Windows (TSPTW) shows evidence indicating that rough-upper-bound and local-bound pruning have a high impact on optimization solvers based on branch-and-bound with MDDs. In particular, it shows that RUB delivers excellent results but requires some effort when defining the model. Also, it shows that LocB provides a significant improvement automatically; without necessitating any user-supplied information. Finally, it also shows that rough-upper-bound and local-bound pruning are not mutually exclusive, and their combined benefit supersedes the individual benefit of using each technique.

We study the problem of performing automated experiment design for drug screening through Bayesian inference and optimisation. In particular, we compare and contrast the behaviour of linear-Gaussian models and Gaussian processes, when used in conjunction with upper confidence bound algorithms, Thompson sampling, or bounded horizon tree search. We show that non-myopic sophisticated exploration techniques using sparse tree search have a distinct advantage over methods such as Thompson sampling or upper confidence bounds in this setting. We demonstrate the significant superiority of the approach over existing and synthetic datasets of drug toxicity.

Best group subset selection aims to choose a small part of non-overlapping groups to achieve the best interpretability on the response variable. It is practically attractive for group variable selection; however, due to the computational intractability in high dimensionality setting, it doesn't catch enough attention. To fill the blank of efficient algorithms for best group subset selection, in this paper, we propose a group-splicing algorithm that iteratively detects effective groups and excludes the helpless ones. Moreover, coupled with a novel Bayesian group information criterion, an adaptive algorithm is developed to determine the true group subset size. It is certifiable that our algorithms enable identifying the optimal group subset in polynomial time under mild conditions. We demonstrate the efficiency and accuracy of our proposal by comparing state-of-the-art algorithms on both synthetic and real-world datasets.

Network spaces have been known as a critical factor in both handcrafted network designs or defining search spaces for Neural Architecture Search (NAS). However, an effective space involves tremendous prior knowledge and/or manual effort, and additional constraints are required to discover efficiency-aware architectures. In this paper, we define a new problem, Network Space Search (NSS), as searching for favorable network spaces instead of a single architecture. We propose an NSS method to directly search for efficient-aware network spaces automatically, reducing the manual effort and immense cost in discovering satisfactory ones. The resultant network spaces, named Elite Spaces, are discovered from Expanded Search Space with minimal human expertise imposed. The Pareto-efficient Elite Spaces are aligned with the Pareto front under various complexity constraints and can be further served as NAS search spaces, benefiting differentiable NAS approaches (e.g. In CIFAR-100, an averagely 2.3% lower error rate and 3.7% closer to target constraint than the baseline with around 90% fewer samples required to find satisfactory networks). Moreover, our NSS approach is capable of searching for superior spaces in future unexplored spaces, revealing great potential in searching for network spaces automatically.

Recent machine-learning approaches to deterministic search and domain-independent planning employ policy learning to speed up search. Unfortunately, when attempting to solve a search problem by successively applying a policy, no guarantees can be given on solution quality. The problem of how to effectively use a learned policy within a bounded-suboptimal search algorithm remains largely as an open question. In this paper, we propose various ways in which such policies can be integrated into Focal Search, assuming that the policy is a neural network classifier. Furthermore, we provide mathematical foundations for some of the resulting algorithms. To evaluate the resulting algorithms over a number of policies with varying accuracy, we use synthetic policies which can be generated for a target accuracy for problems where the search space can be held in memory. We evaluate our focal search variants over three benchmark domains using our synthetic approach, and on the 15-puzzle using a neural network learned using 1.5 million examples. We observe that \emph{Discrepancy Focal Search}, which we show expands the node which maximizes an approximation of the probability that its corresponding path is a prefix of an optimal path, obtains, in general, the best results in terms of runtime and solution quality.

Portfolio methods represent a simple but efficient type of action abstraction which has shown to improve the performance of search-based agents in a range of strategy games. We first review existing portfolio techniques and propose a new algorithm for optimization and action-selection based on the Rolling Horizon Evolutionary Algorithm. Moreover, a series of variants are developed to solve problems in different aspects. We further analyze the performance of discussed agents in a general strategy game-playing task. For this purpose, we run experiments on three different game-modes of the Stratega framework. For the optimization of the agents' parameters and portfolio sets we study the use of the N-tuple Bandit Evolutionary Algorithm. The resulting portfolio sets suggest a high diversity in play-styles while being able to consistently beat the sample agents. An analysis of the agents' performance shows that the proposed algorithm generalizes well to all game-modes and is able to outperform other portfolio methods.

In this article we will explain what index data structures are and introduce you to some popular structures. In today's world, ever-increasing amounts of data are being processed. The data can be used to derive business strategies in a commercial context, but also to gain valuable information about all scientific disciplines. The data obtained must be saved, ideally as raw data, and stored for future analysis. At the time of creation, it is not yet possible to estimate what information might be valuable at some point.