Active learning has shown to reduce the number of experiments needed to obtain high-confidence drug-target predictions. However, in order to actually save experiments using active learning, it is crucial to have a method to evaluate the quality of the current prediction and decide when to stop the experimentation process. Only by applying reliable stoping criteria to active learning, time and costs in the experimental process can be actually saved. We compute active learning traces on simulated drug-target matrices in order to learn a regression model for the accuracy of the active learner. By analyzing the performance of the regression model on simulated data, we design stopping criteria for previously unseen experimental matrices. We demonstrate on four previously characterized drug effect data sets that applying the stopping criteria can result in upto 40% savings of the total experiments for highly accurate predictions.

We show that if $F$ is a convex class of functions that is $L$-subgaussian, the error rate of learning problems generated by independent noise is equivalent to a fixed point determined by `local' covering estimates of the class, rather than by the gaussian averages. To that end, we establish new sharp upper and lower estimates on the error rate for such problems.

Stochastic binary hidden units in a multi-layer perceptron (MLP) network give at least three potential benefits when compared to deterministic MLP networks. (1) They allow to learn one-to-many type of mappings. (2) They can be used in structured prediction problems, where modeling the internal structure of the output is important. (3) Stochasticity has been shown to be an excellent regularizer, which makes generalization performance potentially better in general. However, training stochastic networks is considerably more difficult. We study training using M samples of hidden activations per input. We show that the case M=1 leads to a fundamentally different behavior where the network tries to avoid stochasticity. We propose two new estimators for the training gradient and propose benchmark tests for comparing training algorithms. Our experiments confirm that training stochastic networks is difficult and show that the proposed two estimators perform favorably among all the five known estimators.

Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix obtained by concatenating high-dimensional vectors from a training collection. While the idealized task would be to optimize the expected quality of the factors over the underlying distribution of training vectors, it is achieved in practice by minimizing an empirical average over the considered collection. The focus of this paper is to provide sample complexity estimates to uniformly control how much the empirical average deviates from the expected cost function. Standard arguments imply that the performance of the empirical predictor also exhibit such guarantees. The level of genericity of the approach encompasses several possible constraints on the factors (tensor product structure, shift-invariance, sparsity \ldots), thus providing a unified perspective on the sample complexity of several widely used matrix factorization schemes. The derived generalization bounds behave proportional to $\sqrt{\log(n)/n}$ w.r.t.\ the number of samples $n$ for the considered matrix factorization techniques.

We propose that Solomonoff induction is complete in the physical sense via several strong physical arguments. We also argue that Solomonoff induction is fully applicable to quantum mechanics. We show how to choose an objective reference machine for universal induction by defining a physical message complexity and physical message probability, and argue that this choice dissolves some well-known objections to universal induction. We also introduce many more variants of physical message complexity based on energy and action, and discuss the ramifications of our proposals. "If you wish to make an apple pie from scratch, you must first invent the universe."

Matrix completion has attracted significant recent attention in many fields including statistics, applied mathematics and electrical engineering. Current literature on matrix completion focuses primarily on independent sampling models under which the individual observed entries are sampled independently. Motivated by applications in genomic data integration, we propose a new framework of structured matrix completion (SMC) to treat structured missingness by design. Specifically, our proposed method aims at efficient matrix recovery when a subset of the rows and columns of an approximately low-rank matrix are observed. We provide theoretical justification for the proposed SMC method and derive lower bound for the estimation errors, which together establish the optimal rate of recovery over certain classes of approximately low-rank matrices. Simulation studies show that the method performs well in finite sample under a variety of configurations. The method is applied to integrate several ovarian cancer genomic studies with different extent of genomic measurements, which enables us to construct more accurate prediction rules for ovarian cancer survival.

Regularized training of an autoencoder typically results in hidden unit biases that take on large negative values. We show that negative biases are a natural result of using a hidden layer whose responsibility is to both represent the input data and act as a selection mechanism that ensures sparsity of the representation. We then show that negative biases impede the learning of data distributions whose intrinsic dimensionality is high. We also propose a new activation function that decouples the two roles of the hidden layer and that allows us to learn representations on data with very high intrinsic dimensionality, where standard autoencoders typically fail. Since the decoupled activation function acts like an implicit regularizer, the model can be trained by minimizing the reconstruction error of training data, without requiring any additional regularization.

Protein contacts contain important information for protein structure and functional study, but contact prediction from sequence remains very challenging. Both evolutionary coupling (EC) analysis and supervised machine learning methods are developed to predict contacts, making use of different types of information, respectively. This paper presents a group graphical lasso (GGL) method for contact prediction that integrates joint multi-family EC analysis and supervised learning. Different from existing single-family EC analysis that uses residue co-evolution information in only the target protein family, our joint EC analysis uses residue co-evolution in both the target family and its related families, which may have divergent sequences but similar folds. To implement joint EC analysis, we model a set of related protein families using Gaussian graphical models (GGM) and then co-estimate their precision matrices by maximum-likelihood, subject to the constraint that the precision matrices shall share similar residue co-evolution patterns. To further improve the accuracy of the estimated precision matrices, we employ a supervised learning method to predict contact probability from a variety of evolutionary and non-evolutionary information and then incorporate the predicted probability as prior into our GGL framework. Experiments show that our method can predict contacts much more accurately than existing methods, and that our method performs better on both conserved and family-specific contacts.

We address the collective matrix completion problem of jointly recovering a collection of matrices with shared structure from partial (and potentially noisy) observations. To ensure well--posedness of the problem, we impose a joint low rank structure, wherein each component matrix is low rank and the latent space of the low rank factors corresponding to each entity is shared across the entire collection. We first develop a rigorous algebra for representing and manipulating collective--matrix structure, and identify sufficient conditions for consistent estimation of collective matrices. We then propose a tractable convex estimator for solving the collective matrix completion problem, and provide the first non--trivial theoretical guarantees for consistency of collective matrix completion. We show that under reasonable assumptions stated in Section 3.1, with high probability, the proposed estimator exactly recovers the true matrices whenever sample complexity requirements dictated by Theorem 1 are met. The sample complexity requirement derived in the paper are optimum up to logarithmic factors, and significantly improve upon the requirements obtained by trivial extensions of standard matrix completion. Finally, we propose a scalable approximate algorithm to solve the proposed convex program, and corroborate our results through simulated experiments.

We show that accelerated gradient descent, averaged gradient descent and the heavy-ball method for non-strongly-convex problems may be reformulated as constant parameter second-order difference equation algorithms, where stability of the system is equivalent to convergence at rate O(1/n 2), where n is the number of iterations. We provide a detailed analysis of the eigenvalues of the corresponding linear dynamical system , showing various oscillatory and non-oscillatory behaviors, together with a sharp stability result with explicit constants. We also consider the situation where noisy gradients are available, where we extend our general convergence result, which suggests an alternative algorithm (i.e., with different step sizes) that exhibits the good aspects of both averaging and acceleration.