This paper introduces a simple and efficient density estimator that enables fast systematic search. To show its advantage over commonly used kernel density estimator, we apply it to outlying aspects mining. Outlying aspects mining discovers feature subsets (or subspaces) that describe how a query stand out from a given dataset. The task demands a systematic search of subspaces. We identify that existing outlying aspects miners are restricted to datasets with small data size and dimensions because they employ kernel density estimator, which is computationally expensive, for subspace assessments. We show that a recent outlying aspects miner can run orders of magnitude faster by simply replacing its density estimator with the proposed density estimator, enabling it to deal with large datasets with thousands of dimensions that would otherwise be impossible.

The n-Queens problem is to place n chess queens on an n by n chessboard so that no two queens are on the same row, column or diagonal. The n-Queens Completion problem is a variant, dating to 1850, in which some queens are already placed and the solver is asked to place the rest, if possible. We show that n-Queens Completion is both NP-Complete and #P-Complete. A corollary is that any non-attacking arrangement of queens can be included as a part of a solution to a larger n-Queens problem. We introduce generators of random instances for n-Queens Completion and the closely related Blocked n-Queens and Excluded Diagonals Problem. We describe three solvers for these problems, and empirically analyse the hardness of randomly generated instances. For Blocked n-Queens and the Excluded Diagonals Problem, we show the existence of a phase transition associated with hard instances as has been seen in other NP-Complete problems, but a natural generator for n-Queens Completion did not generate consistently hard instances. The significance of this work is that the n-Queens problem has been very widely used as a benchmark in Artificial Intelligence, but conclusions on it are often disputable because of the simple complexity of the decision problem. Our results give alternative benchmarks which are hard theoretically and empirically, but for which solving techniques designed for n-Queens need minimal or no change.

"Consumers who expect to receive plaintiff's Rubik's Cube puzzle, for which plaintiff has developed a national and international reputation, will be disappointed when using defendants' imitation," which causes "irreparable harm" to Rubik's Brand's reputation and goodwill, the complaint said.

Bipartite matching, where agents on one side of a market are matched to agents or items on the other, is a classical problem in computer science and economics, with widespread application in healthcare, education, advertising, and general resource allocation. A practitioner's goal is typically to maximize a matching market's economic efficiency, possibly subject to some fairness requirements that promote equal access to resources. A natural balancing act exists between fairness and efficiency in matching markets, and has been the subject of much research. In this paper, we study a complementary goal-- balancing diversity and efficiency--in a generalization of bipartite matching where agents on one side of the market can be matched to sets of agents on the other. Adapting a classical definition of the diversity of a set, we propose a quadratic programming-based approach to solving a supermodular minimization problem that balances diversity and total weight of the solution. We also provide a scalable greedy algorithm with theoretical performance bounds. We then define the price of diversity, a measure of the efficiency loss due to enforcing diversity, and give a worst-case theoretical bound. Finally, we demonstrate the efficacy of our methods on three real-world datasets, and show that the price of diversity is not bad in practice. Our code is publicly accessible for further research.

From medicines to materials, small organic molecules are indispensable for human well-being. To plan their syntheses, chemists employ a problem solving technique called retrosynthesis. In retrosynthesis, target molecules are recursively transformed into increasingly simpler precursor compounds until a set of readily available starting materials is obtained. Computer-aided retrosynthesis would be a highly valuable tool, however, past approaches were slow and provided results of unsatisfactory quality. Here, we employ Monte Carlo Tree Search (MCTS) to efficiently discover retrosynthetic routes. MCTS was combined with an expansion policy network that guides the search, and an "in-scope" filter network to pre-select the most promising retrosynthetic steps. These deep neural networks were trained on 12 million reactions, which represents essentially all reactions ever published in organic chemistry. Our system solves almost twice as many molecules and is 30 times faster in comparison to the traditional search method based on extracted rules and hand-coded heuristics. Finally after a 60 year history of computer-aided synthesis planning, chemists can no longer distinguish between routes generated by a computer system and real routes taken from the scientific literature. We anticipate that our method will accelerate drug and materials discovery by assisting chemists to plan better syntheses faster, and by enabling fully automated robot synthesis.

Despite large incentives, correctness in software remains an elusive goal. Declarative programming techniques, where algorithms are derived from a specification of the desired behavior, offer hope to address this problem, since there is a combinatorial reduction in complexity in programming in terms of specifications instead of algorithms, and arbitrary desired properties can be expressed and enforced in specifications directly. However, limitations on performance have prevented programming with declarative specifications from becoming a mainstream technique for general-purpose programming. To address the performance bottleneck in deriving an algorithm from a specification, I propose information-gain computation, a framework where an adaptive evaluation strategy is used to efficiently perform a search which derives algorithms that provide information about a query via the most efficient routes. Within this framework, opportunities to compress the search space present themselves, which suggest that information-theoretic bounds on the performance of such a system might be articulated and a system designed to achieve them. In a preliminary empirical study of adaptive evaluation for a simple test program, the evaluation strategy adapts successfully to evaluate a query efficiently.

The negative gradient tells us that there is an inverse relationship between mpg and displacement with one unit increase in displacement resulting in a 0.04 unit decrease in mpg. How are these intercept and gradient values calculated one may ask? Each set of xy data points are iterated over to find the squared error, all squared errors are summed and the sum is divided by n to get the MSE. Next, we can calculate the MSE by summing the squared differences between observed yvalues and our predicted y values then dividing by the number of observations n. This gives a MSE of 9.911209 for this linear model.

Sensing in complex systems requires large-scale information exchange and on-the-go communications over heterogeneous networks and integrated processing platforms. Many networked cyber-physical systems exhibit hierarchical infrastructures of information flows, which naturally leads to a multi-level tree-like information structure in which each level corresponds to a particular scale of representation. This work focuses on the multiscale fusion of data collected at multiple levels of the system. We propose a multiscale state-space model to represent multi-resolution data over the hierarchical information system and formulate a multi-stage dynamic zero-sum game to design a multi-scale $H_{\infty}$ robust filter. We present numerical experiments for one and two-dimensional signals and provide a comparative analysis of the minimax filter with the standard Kalman filter to show the improvement in signal-to-noise ratio (SNR).

The goal of Machine Learning to automatically learn from data, extract knowledge and to make decisions without any human intervention. Such automatic (aML) approaches show impressive success. Recent results even demonstrate intriguingly that deep learning applied for automatic classification of skin lesions is on par with the performance of dermatologists, yet outperforms the average. As human perception is inherently limited, such approaches can discover patterns, e.g. that two objects are similar, in arbitrarily high-dimensional spaces what no human is able to do. Humans can deal only with limited amounts of data, whilst big data is beneficial for aML; however, in health informatics, we are often confronted with a small number of data sets, where aML suffer of insufficient training samples and many problems are computationally hard. Here, interactive machine learning (iML) may be of help, where a human-in-the-loop contributes to reduce the complexity of NP-hard problems. A further motivation for iML is that standard black-box approaches lack transparency, hence do not foster trust and acceptance of ML among end-users. Rising legal and privacy aspects, e.g. with the new European General Data Protection Regulations, make black-box approaches difficult to use, because they often are not able to explain why a decision has been made. In this paper, we present some experiments to demonstrate the effectiveness of the human-in-the-loop approach, particularly in opening the black-box to a glass-box and thus enabling a human directly to interact with an learning algorithm. We selected the Ant Colony Optimization framework, and applied it on the Traveling Salesman Problem, which is a good example, due to its relevance for health informatics, e.g. for the study of protein folding. From studies of how humans extract so much from so little data, fundamental ML-research also may benefit.

Wireless systems perform rate adaptation to transmit at highest possible instantaneous rates. Rate adaptation has been increasingly granular over generations of wireless systems. The base-station uses SINR and packet decode feedback called acknowledgement/no acknowledgement (ACK/NACK) to perform rate adaptation. SINR is used for rate anchoring called inner look adaptation and ACK/NACK is used for fine offset adjustments called Outer Loop Link Adaptation (OLLA). We cast the OLLA as a reinforcement learning problem of the class of Multi-Armed Bandits (MAB) where the different offset values are the arms of the bandit. In OLLA, as the offset values increase, the probability of packet error also increase, and every user equipment (UE) has a desired Block Error Rate (BLER) to meet certain Quality of Service (QoS) requirements. For this MAB we propose a binary search based algorithm which achieves a Probably Approximately Correct (PAC) solution making use of bounds from large deviation theory and confidence bounds. In addition to this we also discuss how a Thompson sampling or UCB based method will not help us meet the target objectives. Finally, simulation results are provided on an LTE system simulator and thereby prove the efficacy of our proposed algorithm.