Action abstractions restrict the number of legal actions available during search in multi-unit real-time adversarial games, thus allowing algorithms to focus their search on a set of promising actions. Optimal strategies derived from un-abstracted spaces are guaranteed to be no worse than optimal strategies derived from action-abstracted spaces. In practice, however, due to real-time constraints and the state space size, one is only able to derive good strategies in un-abstracted spaces in small-scale games. In this paper we introduce search algorithms that use an action abstraction scheme we call asymmetric abstraction. Asymmetric abstractions retain the un-abstracted spaces' theoretical advantage over regularly abstracted spaces while still allowing the search algorithms to derive effective strategies, even in large-scale games. Empirical results on combat scenarios that arise in a real-time strategy game show that our search algorithms are able to substantially outperform state-of-the-art approaches.

There are two major approaches for structured classification. One is the probabilistic gradient-based methods such as conditional random fields (CRF), which has high accuracy but with drawbacks: slow training, and no support of search-based optimization (which is important in many cases). The other one is the search-based learning methods such as perceptrons and margin infused relaxed algorithm (MIRA), which have fast training but also with drawbacks: low accuracy, no probabilistic information, and non-convergence in real-world tasks. We propose a novel and "shockingly easy" solution, a search-based probabilistic online learning method, to address most of those issues. This method searches the output candidates, derives probabilities, and conduct efficient online learning. We show that this method is with fast training, support search-based optimization, very easy to implement, with top accuracy, with probabilities, and with theoretical guarantees of convergence. Experiments on well-known tasks show that our method has better accuracy than CRF and almost as fast training speed as perceptron and MIRA. Results also show that SAPO can easily beat the state-of-the-art systems on those highly-competitive tasks, achieving record-breaking accuracies. The codes can be found at https://github.com/lancopku

This paper presents a framework for exact discovery of the top-k sequential patterns under Leverage. It combines (1) a novel definition of the expected support for a sequential pattern - a concept on which most interestingness measures directly rely - with (2) SkOPUS: a new branch-and-bound algorithm for the exact discovery of top-k sequential patterns under a given measure of interest. Our interestingness measure employs the partition approach. A pattern is interesting to the extent that it is more frequent than can be explained by assuming independence between any of the pairs of patterns from which it can be composed. The larger the support compared to the expectation under independence, the more interesting is the pattern. We build on these two elements to exactly extract the k sequential patterns with highest leverage, consistent with our definition of expected support. We conduct experiments on both synthetic data with known patterns and real-world datasets; both experiments confirm the consistency and relevance of our approach with regard to the state of the art. This article was published in Data Mining and Knowledge Discovery and is accessible at http://dx.doi.org/10.1007/s10618-016-0467-9.

Community detection in hypergraphs is explored. Under a generative hypergraph model called "d-wise hypergraph stochastic block model" (d-hSBM) which naturally extends the Stochastic Block Model from graphs to d-uniform hypergraphs, the asymptotic minimax mismatch ratio is characterized. For proving the achievability, we propose a two-step polynomial time algorithm that achieves the fundamental limit. The first step of the algorithm is a hypergraph spectral clustering method which achieves partial recovery to a certain precision level. The second step is a local refinement method which leverages the underlying probabilistic model along with parameter estimation from the outcome of the first step. To characterize the asymptotic performance of the proposed algorithm, we first derive a sufficient condition for attaining weak consistency in the hypergraph spectral clustering step. Then, under the guarantee of weak consistency in the first step, we upper bound the worst-case risk attained in the local refinement step by an exponentially decaying function of the size of the hypergraph and characterize the decaying rate. For proving the converse, the lower bound of the minimax mismatch ratio is set by finding a smaller parameter space which contains the most dominant error events, inspired by the analysis in the achievability part. It turns out that the minimax mismatch ratio decays exponentially fast to zero as the number of nodes tends to infinity, and the rate function is a weighted combination of several divergence terms, each of which is the Renyi divergence of order 1/2 between two Bernoulli's. The Bernoulli's involved in the characterization of the rate function are those governing the random instantiation of hyperedges in d-hSBM. Experimental results on synthetic data validate our theoretical finding that the refinement step is critical in achieving the optimal statistical limit.

A machine learning model is itself parameterised by a large number of different parameters (e.g., learning rate, number of hidden units, strength of weight regularization). How you set these hyper-parameters can have a big impact on the overall results achieved, but finding an optimal set of hyper-parameters is far from easy. Essentially it boils down to picking some sets of parameters and trying them to see how well they work. How do you choose which sets to pick though? Even with a relatively small number of parameters it's impossible to do an exhaustive search as the search space grows exponentially with the number of hyper-parameters.

Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose to quantify the estimation loss of CCA by the excess prediction loss defined through a prediction-after-dimension-reduction framework. Such framework suggests viewing CCA estimation as estimating the subspaces spanned by the canonical variates. Interestedly, the proposed error metrics derived from the excess prediction loss turn out to be closely related to the principal angles between the subspaces spanned by the population and sample canonical variates respectively. We characterize the non-asymptotic minimax rates under the proposed metrics, especially the dependency of the minimax rates on the key quantities including the dimensions, the condition number of the covariance matrices, the canonical correlations and the eigen-gap, with minimal assumptions on the joint covariance matrix. To the best of our knowledge, this is the first finite sample result that captures the effect of the canonical correlations on the minimax rates.

The purpose of this project is to design and implement a game playing agent to play a game using adversarial search methods. The goal is to create a game playing agent that defeats our opponent at a game of isolation consistently. For this project I've designed three heuristics to create an effective edge for the game playing agent. Don't know what Isolation is? Check out out this page: isolation.secdevops.ai and compete against my agent. In the case of the game isolation, there are two players competing against each other.

While advances in computing resources have made processing enormous amounts of data possible, human ability to identify patterns in such data has not scaled accordingly. Efficient computational methods for condensing and simplifying data are thus becoming vital for extracting actionable insights. In particular, while data summarization techniques have been studied extensively, only recently has summarizing interconnected data, or graphs, become popular. This survey is a structured, comprehensive overview of the state-of-the-art methods for summarizing graph data. We first broach the motivation behind, and the challenges of, graph summarization. We then categorize summarization approaches by the type of graphs taken as input and further organize each category by core methodology. Finally, we discuss applications of summarization on real-world graphs and conclude by describing some open problems in the field.

Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank \cite{Frank1978} of estimating the number of connected components in a large graph based on the subgraph sampling model, in which we randomly sample a subset of the vertices and observe the induced subgraph. The key question is whether accurate estimation is achievable in the \emph{sublinear} regime where only a vanishing fraction of the vertices are sampled. We show that it is impossible if the parent graph is allowed to contain high-degree vertices or long induced cycles. For the class of chordal graphs, where induced cycles of length four or above are forbidden, we characterize the optimal sample complexity within constant factors and construct linear-time estimators that provably achieve these bounds. This significantly expands the scope of previous results which have focused on unbiased estimators and special classes of graphs such as forests or cliques. Both the construction and the analysis of the proposed methodology rely on combinatorial properties of chordal graphs and identities of induced subgraph counts. They, in turn, also play a key role in proving minimax lower bounds based on construction of random instances of graphs with matching structures of small subgraphs.

In this work we explore the use of metric index structures, which accelerate nearest neighbor queries, in the scenario where we need to interleave insertions and queries during deployment. This use-case is inspired by a real-life need in malware analysis triage, and is surprisingly understudied. Existing literature tends to either focus on only final query efficiency, often does not support incremental insertion, or does not support arbitrary distance metrics. We modify and improve three algorithms to support our scenario of incremental insertion and querying with arbitrary metrics, and evaluate them on multiple datasets and distance metrics while varying the value of $k$ for the desired number of nearest neighbors. In doing so we determine that our improved Vantage-Point tree of Minimum-Variance performs best for this scenario.