Rating Prediction is a basic problem in Recommender System, and one of the most widely used method is Factorization Machines(FM). However, traditional matrix factorization methods fail to utilize the benefit of implicit feedback, which has been proved to be important in Rating Prediction problem. In this work, we consider a specific situation, movie rating prediction, where we assume that a user's watching history has a big influence on his/her rating behavior on an item. We introduce two models, Latent Dirichlet Allocation(LDA) and word2vec, both of which perform state-of-the-art results in training latent features. Based on that, we propose two feature based models. One is the Topic-based FM Model which provides the implicit feedback to the matrix factorization, the other is the Vector-based FM Model which exploits the order info of a user's watching history resulting in better performance. Empirical results on three datasets demonstrate that our method performs better than the baseline model and confirm that Vector-based FM Model usually works better as it contains the order info.

Liquid chromatography coupled with tandem mass spectrometry, also known as shotgun proteomics, is a widely-used high-throughput technology for identifying proteins in complex biological samples. Analysis of the tens of thousands of fragmentation spectra produced by a typical shotgun proteomics experiment begins by assigning to each observed spectrum the peptide hypothesized to be responsible for generating the spectrum, typically done by searching each spectrum against a database of peptides. We have recently described a machine learning method---Dynamic Bayesian Network for Rapid Identification of Peptides (DRIP)---that not only achieves state-of-the-art spectrum identification performance on a variety of datasets but also provides a trainable model capable of returning valuable auxiliary information regarding specific peptide-spectrum matches. In this work, we present two significant improvements to DRIP. First, we describe how to use word lattices, which are widely used in natural language processing, to significantly speed up DRIP's computations. To our knowledge, all existing shotgun proteomics search engines compute independent scores between a given observed spectrum and each possible candidate peptide from the database. The key idea of the word lattice is to represent the set of candidate peptides in a single data structure, thereby allowing sharing of redundant computations among the different candidates. We demonstrate that using lattices in conjunction with DRIP leads to speedups on the order of tens across yeast and worm data sets. Second, we introduce a variant of DRIP that uses a discriminative training framework, performing maximum mutual entropy estimation rather than maximum likelihood estimation. This modification improves DRIP's statistical power, enabling us to increase the number of identified spectrum at a 1% false discovery rate on yeast and worm data sets.

Multi-agent Pathfinding is a relevant problem in a wide range of domains, for example in robotics and video games research. Formally, the problem considers a graph consisting of vertices and edges, and a set of agents occupying vertices. An agent can only move to an unoccupied, neighbouring vertex, and the problem of finding the minimal sequence of moves to transfer each agent from its start location to its destination is an NP-hard problem. We present Push and Rotate, a new algorithm that is complete for Multi-agent Pathfinding problems in which there are at least two empty vertices. Push and Rotate first divides the graph into subgraphs within which it is possible for agents to reach any position of the subgraph, and then uses the simple push, swap, and rotate operations to find a solution; a post-processing algorithm is also presented that eliminates redundant moves. Push and Rotate can be seen as extending Luna and Bekris's Push and Swap algorithm, which we showed to be incomplete in a previous publication. In our experiments we compare our approach with the Push and Swap, MAPP, and Bibox algorithms. The latter algorithm is restricted to a smaller class of instances as it requires biconnected graphs, but can nevertheless be considered state of the art due to its strong performance. Our experiments show that Push and Swap suffers from incompleteness, MAPP is generally not competitive with Push and Rotate, and Bibox is better than Push and Rotate on randomly generated biconnected instances, while Push and Rotate performs better on grids.

We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of low-rank matrices, and the set of sparse matrices; each projection is {\em non-convex} but easy to compute. In spite of this non-convexity, we establish exact recovery of the low-rank matrix, under the same conditions that are required by existing methods (which are based on convex optimization). For an $m \times n$ input matrix ($m \leq n)$, our method has a running time of $O(r^2mn)$ per iteration, and needs $O(\log(1/\epsilon))$ iterations to reach an accuracy of $\epsilon$. This is close to the running time of simple PCA via the power method, which requires $O(rmn)$ per iteration, and $O(\log(1/\epsilon))$ iterations. In contrast, existing methods for robust PCA, which are based on convex optimization, have $O(m^2n)$ complexity per iteration, and take $O(1/\epsilon)$ iterations, i.e., exponentially more iterations for the same accuracy. Experiments on both synthetic and real data establishes the improved speed and accuracy of our method over existing convex implementations.

Modeling dynamical systems is important in many disciplines, e.g., control, robotics, or neurotechnology. Commonly the state of these systems is not directly observed, but only available through noisy and potentially high-dimensional observations. In these cases, system identification, i.e., finding the measurement mapping and the transition mapping (system dynamics) in latent space can be challenging. For linear system dynamics and measurement mappings efficient solutions for system identification are available. However, in practical applications, the linearity assumptions does not hold, requiring non-linear system identification techniques. If additionally the observations are high-dimensional (e.g., images), non-linear system identification is inherently hard. To address the problem of non-linear system identification from high-dimensional observations, we combine recent advances in deep learning and system identification. In particular, we jointly learn a low-dimensional embedding of the observation by means of deep auto-encoders and a predictive transition model in this low-dimensional space. We demonstrate that our model enables learning good predictive models of dynamical systems from pixel information only.

We propose a novel graphical model selection (GMS) scheme for high-dimensional stationary time series or discrete time process. The method is based on a natural generalization of the graphical LASSO (gLASSO), introduced originally for GMS based on i.i.d. samples, and estimates the conditional independence graph (CIG) of a time series from a finite length observation. The gLASSO for time series is defined as the solution of an l1-regularized maximum (approximate) likelihood problem. We solve this optimization problem using the alternating direction method of multipliers (ADMM). Our approach is nonparametric as we do not assume a finite dimensional (e.g., an autoregressive) parametric model for the observed process. Instead, we require the process to be sufficiently smooth in the spectral domain. For Gaussian processes, we characterize the performance of our method theoretically by deriving an upper bound on the probability that our algorithm fails to correctly identify the CIG. Numerical experiments demonstrate the ability of our method to recover the correct CIG from a limited amount of samples.

We study a novel spline-like basis, which we name the "falling factorial basis", bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations in basis matrix multiplication and basis matrix inversion. The falling factorial functions are not actually splines, but are close enough to splines that they provably retain some of the favorable properties of the latter functions. We examine their application in two problems: trend filtering over arbitrary input points, and a higher-order variant of the two-sample Kolmogorov-Smirnov test.

Advances of modern sensing and sequencing technologies generate a deluge of high dimensional space-temporal physiological and next-generation sequencing (NGS) data. Physiological traits are observed either as continuous random functions, or on a dense grid and referred to as function-valued traits. Both physiological and NGS data are highly correlated data with their inherent order, spacing, and functional nature which are ignored by traditional summary-based univariate and multivariate regression methods designed for quantitative genetic analysis of scalar trait and common variants. To capture morphological and dynamic features of the data and utilize their dependent structure, we propose a functional linear model (FLM) in which a trait curve is modeled as a response function, the genetic variation in a genomic region or gene is modeled as a functional predictor, and the genetic effects are modeled as a function of both time and genomic position (FLMF) for genetic analysis of function-valued trait with both GWAS and NGS data. By extensive simulations, we demonstrate that the FLMF has the correct type 1 error rates and much higher power to detect association than the existing methods. The FLMF is applied to sleep data from Starr County health studies where oxygen saturation were measured in 22,670 seconds on average for 833 individuals. We found 65 genes that were significantly associated with oxygen saturation functional trait with P-values ranging from 2.40E-06 to 2.53E-21. The results clearly demonstrate that the FLMF substantially outperforms the traditional genetic models with scalar trait.

We demonstrate that there is significant redundancy in the parameterization of several deep learning models. Given only a few weight values for each feature it is possible to accurately predict the remaining values. Moreover, we show that not only can the parameter values be predicted, but many of them need not be learned at all. We train several different architectures by learning only a small number of weights and predicting the rest. In the best case we are able to predict more than 95% of the weights of a network without any drop in accuracy.

The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the proofs, producing an AI system capable of answering a wide range of mathematical queries automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39% of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped first-order, polymorphic typed first-order, and typed higher-order, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided.