In predicate invention (PI), new predicates are introduced into a logical theory, usually by rewriting a group of closely-related rules to use a common invented predicate as a "subroutine". PI is difficult, since a poorly-chosen invented predicate may lead to error cascades. Here we suggest a "soft" version of predicate invention: instead of explicitly creating new predicates, we implicitly group closely-related rules by using structured sparsity to regularize their parameters together. We show that soft PI, unlike hard PI, consistently improves over previous strong baselines for structure-learning on two large-scale tasks.

Multimodal hashing is essential to cross-media similarity search for its low storage cost and fast query speed. Most existing multimodal hashing methods embedded heterogeneous data into a common low-dimensional Hamming space, and then rounded the continuous embeddings to obtain the binary codes. Yet they usually neglect the inherent discrete nature of hashing for relaxing the discrete constraints, which will cause degraded retrieval performance especially for long codes. For this purpose, a novel Semantic Topic Multimodal Hashing (STMH) is developed by considering latent semantic information in coding procedure. It first discovers clustering patterns of texts and robust factorizes the matrix of images to obtain multiple semantic topics of texts and concepts of images. Then the learned multimodal semantic features are transformed into a common subspace by their correlations. Finally, each bit of unified hash code can be generated directly by figuring out whether a topic or concept is contained in a text or an image. Therefore, the obtained model by STMH is more suitable for hashing scheme as it directly learns discrete hash codes in the coding process. Experimental results demonstrate that the proposed method outperforms several state-of-the-art methods.

We introduce a novel framework for option discovery and learning transfer in complex domains that are represented as object-oriented Markov decision processes (OO-MDPs) [Diuk et al., 2008]. Our framework, Portable Option Discovery (POD), extends existing option discovery methods, and enables transfer across related but different domains by providing an unsupervised method for finding a mapping between object-oriented domains with different state spaces. The framework also includes heuristic approaches for increasing the efficiency of the mapping process. We present the results of applying POD to Pickett and Barto's [2002] PolicyBlocks and MacGlashan's [2013] Option-Based Policy Transfer in two application domains. We show that our approach can discover options effectively, transfer options among different domains, and improve learning performance with low computational overhead.

It is also useful for scientific discovery like in neuroscience, like correlation of X, Y only test for (univariate) to see if a stimulus X (say an image) is independent linear independence, natural alternatives like of the brain activity Y (say fMRI) in a relevant part of mutual information of X, Y are hard to estimate the brain. Since detecting nonlinear correlations is much easier due to a serious curse of dimensionality. A recent than estimating a nonparametric regression function (of approach, avoiding both issues, estimates norms of Y onto X), it can be done at smaller sample sizes, with further an operator in Reproducing Kernel Hilbert Spaces samples collected for estimation only if an effect is detected (RKHSs). Our main contribution is strong empirical by the hypothesis test. For such situations, correlation evidence that by employing shrunk operators only tests for univariate linear independence, while other when the sample size is small, one can attain an improvement statistics like mutual information that do characterize multivariate in power at low false positive rates. We independence are hard to estimate from data, suffering analyze the effects of Stein shrinkage on a popular from a serious curse of dimensionality. A recent popular test statistic called HSIC (Hilbert-Schmidt Independence approach for this problem (and a related two-sample testing Criterion). Our observations provide insights problem) involve the use of quantities defined in reproducing into two recently proposed shrinkage estimators, kernel Hilbert spaces (RKHSs) - see [Gretton et al., 2006; SCOSE and FCOSE - we prove that SCOSE Harchaoui et al., 2007; Gretton et al., 2005b; 2005a].

Tensor factorization methods provide a useful way to extract latent factors from complex multirelational data, and also for predicting missing data. Developing tensor factorization methods for massive tensors, especially when the data are binary- or count-valued (which is true of most real-world tensors), however, remains a challenge. We develop a scalable probabilistic tensor factorization framework that enables us to perform efficient factorization of massive binary and count tensor data. The framework is based on (i) the Polya-Gamma augmentation strategy which makes the model fully locally conjugate and allows closed-form parameter updates when data are binary- or count-valued; and (ii) an efficient online Expectation Maximization algorithm, which allows processing data in small mini-batches, and facilitates handling massive tensor data. Moreover, various types of constraints on the factor matrices (e.g., sparsity, non-negativity) can be incorporated under the proposed framework, providing good interpretability, which can be useful for qualitative analyses of the results. We apply the proposed framework on analyzing several binary- and count-valued real-world data sets.

Gaussian processes (GPs) provide a nonparametric representation of functions. However, classical GP inference suffers from high computational cost for big data. In this paper, we propose a new Bayesian approach, EigenGP, that learns both basis dictionary elements — eigenfunctions of a GP prior — and prior precisions in a sparse finite model. It is well known that, among all orthogonal basis functions, eigenfunctions can provide the most compact representation. Unlike other sparse Bayesian finite models where the basis function has a fixed form, our eigenfunctions live in a reproducing kernel Hilbert space as a finite linear combination of kernel functions. We learn the dictionary elements — eigenfunctions — and the prior precisions over these elements as well as all the other hyperparameters from data by maximizing the model marginal likelihood. We explore computational linear algebra to simplify the gradient computation significantly. Our experimental results demonstrate improved predictive performance of EigenGP over alternative sparse GP methods as well as relevance vector machines.

Science ultimately seeks to reliably predict aspects of the future; but, how is this even possible in light of the logical paradox that making a prediction may cause the world to evolve in a manner that defeats it? We show how learning can naturally resolve this conundrum. The problem is studied within a causal or temporal version of the Probably Approximately Correct semantics, extended so that a learner's predictions are first recorded in the states upon which the learned hypothesis is later applied. On the negative side, we make concrete the intuitive impossibility of predicting reliably, even under very weak assumptions. On the positive side, we identify conditions under which a generic learning schema, akin to randomized trials, supports agnostic learnability.

Kernel SVM suffers from high computational complexity when dealing with large-scale nonlinear datasets. To address this issue, locally linear classifiers have been proposed for approximating nonlinear decision boundaries with locally linear functions using a local coding scheme. The effectiveness of such coding scheme depends heavily on the quality of anchor points chosen to produce the local codes. Existing methods usually involve a phase of unsupervised anchor point learning followed by supervised classifier learning. Thus, the anchor points and classifiers are obtained separately whereas the learned anchor points may not be optimal for the discriminative task. In this paper, we present a novel fully supervised approach for anchor point learning. A single optimization problem is formulated over both anchor point and classifier variables, optimizing the initial anchor points jointly with the classifiers to minimize the classification risk. Experimental results show that our method outperforms other competitive methods which employ unsupervised anchor point learning and achieves performance on par with the kernel SVM albeit with much improved efficiency.

Kernel sparse coding is an effective strategy to capturethe non-linear structure of data samples. However,how to learn a robust kernel dictionary remainsan open problem. In this paper, we propose a new optimization model to learn the robust kernel dictionary while isolating outliers in the training samples. This model is essentially based on the decomposition of the reconstruction error into small dense noises and large sparse outliers. The outliererror term is formulated as the product of the sample matrix in the feature space and a diagonal coefficient matrix. This facilitates the kernelized dictionary learning. To solve the non-convex optimization problem, we develop a whole sequence convergent algorithm which guarantees the obtained solution sequence is a Cauchy sequence. The experimental results show that the proposed robust kernel dictionary learning method provides significant performance improvement.

Given several tasks, multi-task learning (MTL) learns multiple tasks jointly by exploring the interdependence between them. The basic assumption in MTL is that those tasks are indeed related. Existing MTL methods model the task relatedness/interdependence in two different ways, either common parameter-sharing or common feature-sharing across tasks. In this paper, we propose a novel multi-task learning method to jointly learn shared parameters and shared feature representation. Our objective is to learn a set of common features with which the tasks are related as closely as possible, therefore common parameters shared across tasks can be optimally learned. We present a detailed deviation of our multi-task learning method and propose an alternating algorithm to solve the non-convex optimization problem. We further present a theoretical bound which directly demonstrates that the proposed multi-task learning method can successfully model the relatedness via joint common parameter- and common feature-learning. Extensive experiments are conducted on several real world multi-task learning datasets. All results demonstrate the effectiveness of our multi-task model and feature joint learning method.