With data collection on the rise, machine learning is a hot topic. The manner in which computers are able to mimic human thinking is rapidly exceeding human capabilities in everything from chess to picking the winner of a song contest.

Data is the lifeblood of any business. And while advances in machine learning have been revolutionizing almost every industry, some have lagged behind due to technical constraints. Healthcare and life sciences rely on information, but when it comes to data, many professionals in this arena are stuck with legacy technologies when conducting their research. As John Brownstein, Director of the Computational Epidemiology Group at the Boston Children's Hospital put it, "We're missing the data, we're missing the realtime information, we're missing the forecasting methods. And we're missing the consumer tools that feed back to the patient to inform us about what's happening around us."

Iterative Hard Thresholding (IHT) is a class of projected gradient descent methods for optimizing sparsity-constrained minimization models, with the best known efficiency and scalability in practice. As far as we know, the existing IHT-style methods are designed for sparse minimization in primal form. It remains open to explore duality theory and algorithms in such a non-convex and NP-hard problem setting. In this paper, we bridge this gap by establishing a duality theory for sparsity-constrained minimization with $\ell_2$-regularized loss function and proposing an IHT-style algorithm for dual maximization. Our sparse duality theory provides a set of sufficient and necessary conditions under which the original NP-hard/non-convex problem can be equivalently solved in a dual formulation. The proposed dual IHT algorithm is a super-gradient method for maximizing the non-smooth dual objective. An interesting finding is that the sparse recovery performance of dual IHT is invariant to the Restricted Isometry Property (RIP), which is required by virtually all the existing primal IHT algorithms without sparsity relaxation. Moreover, a stochastic variant of dual IHT is proposed for large-scale stochastic optimization. Numerical results demonstrate the superiority of dual IHT algorithms to the state-of-the-art primal IHT-style algorithms in model estimation accuracy and computational efficiency.

Machine-learned models are often described as "black boxes". In many real-world applications however, models may have to sacrifice predictive power in favour of human-interpretability. When this is the case, feature engineering becomes a crucial task, which requires significant and time-consuming human effort. Whilst some features are inherently static, representing properties that cannot be influenced (e.g., the age of an individual), others capture characteristics that could be adjusted (e.g., the daily amount of carbohydrates taken). Nonetheless, once a model is learned from the data, each prediction it makes on new instances is irreversible - assuming every instance to be a static point located in the chosen feature space. There are many circumstances however where it is important to understand (i) why a model outputs a certain prediction on a given instance, (ii) which adjustable features of that instance should be modified, and finally (iii) how to alter such a prediction when the mutated instance is input back to the model. In this paper, we present a technique that exploits the internals of a tree-based ensemble classifier to offer recommendations for transforming true negative instances into positively predicted ones. We demonstrate the validity of our approach using an online advertising application. First, we design a Random Forest classifier that effectively separates between two types of ads: low (negative) and high (positive) quality ads (instances). Then, we introduce an algorithm that provides recommendations that aim to transform a low quality ad (negative instance) into a high quality one (positive instance). Finally, we evaluate our approach on a subset of the active inventory of a large ad network, Yahoo Gemini.

Node-perturbation learning is a type of statistical gradient descent algorithm that can be applied to problems where the objective function is not explicitly formulated, including reinforcement learning. It estimates the gradient of an objective function by using the change in the object function in response to the perturbation. The value of the objective function for an unperturbed output is called a baseline. Cho et al. proposed node-perturbation learning with a noisy baseline. In this paper, we report on building the statistical mechanics of Cho's model and on deriving coupled differential equations of order parameters that depict learning dynamics. We also show how to derive the generalization error by solving the differential equations of order parameters. On the basis of the results, we show that Cho's results are also apply in general cases and show some general performances of Cho's model.

Deep learning is the state-of-the-art in fields such as visual object recognition and speech recognition. This learning uses a large number of layers, huge number of units, and connections. Therefore, overfitting is a serious problem. To avoid this problem, dropout learning is proposed. Dropout learning neglects some inputs and hidden units in the learning process with a probability, p, and then, the neglected inputs and hidden units are combined with the learned network to express the final output. We find that the process of combining the neglected hidden units with the learned network can be regarded as ensemble learning, so we analyze dropout learning from this point of view.

In the last few years, we have seen the transformative impact of deep learning in many applications, particularly in speech recognition and computer vision. Inspired by Google's Inception-ResNet deep convolutional neural network (CNN) for image classification, we have developed "Chemception", a deep CNN for the prediction of chemical properties, using just the images of 2D drawings of molecules. We develop Chemception without providing any additional explicit chemistry knowledge, such as basic concepts like periodicity, or advanced features like molecular descriptors and fingerprints. We then show how Chemception can serve as a general-purpose neural network architecture for predicting toxicity, activity, and solvation properties when trained on a modest database of 600 to 40,000 compounds. When compared to multi-layer perceptron (MLP) deep neural networks trained with ECFP fingerprints, Chemception slightly outperforms in activity and solvation prediction and slightly underperforms in toxicity prediction. Having matched the performance of expert-developed QSAR/QSPR deep learning models, our work demonstrates the plausibility of using deep neural networks to assist in computational chemistry research, where the feature engineering process is performed primarily by a deep learning algorithm.

Undetected overfitting can occur when there are significant redundancies between training and validation data. We describe AVE, a new measure of training-validation redundancy for ligand-based classification problems that accounts for the similarity amongst inactive molecules as well as active. We investigated nine widely-used benchmarks for virtual screening and QSAR, and show that the amount of AVE bias strongly correlates with the performance of ligand-based predictive methods irrespective of the predicted property, chemical fingerprint, similarity measure, or previously-applied unbiasing techniques. Therefore, it is likely that the previously-reported performance of most ligand-based methods can be explained by overfitting to benchmarks rather than good prospective accuracy.

We describe a framework for deriving and analyzing online optimization algorithms that incorporate adaptive, data-dependent regularization, also termed preconditioning. Such algorithms have been proven useful in stochastic optimization by reshaping the gradients according to the geometry of the data. Our framework captures and unifies much of the existing literature on adaptive online methods, including the AdaGrad and Online Newton Step algorithms as well as their diagonal versions. As a result, we obtain new convergence proofs for these algorithms that are substantially simpler than previous analyses. Our framework also exposes the rationale for the different preconditioned updates used in common stochastic optimization methods.

Deep generative networks provide a powerful tool for modeling complex data in a wide range of applications. In inverse problems that use these networks as generative priors on data, one must often perform inference of the inputs of the networks from the outputs. Inference is also required for sampling during stochastic training on these generative models. This paper considers inference in a deep stochastic neural network where the parameters (e.g., weights, biases and activation functions) are known and the problem is to estimate the values of the input and hidden units from the output. While several approximate algorithms have been proposed for this task, there are few analytic tools that can provide rigorous guarantees in the reconstruction error. This work presents a novel and computationally tractable output-to-input inference method called Multi-Layer Vector Approximate Message Passing (ML-VAMP). The proposed algorithm, derived from expectation propagation, extends earlier AMP methods that are known to achieve the replica predictions for optimality in simple linear inverse problems. Our main contribution shows that the mean-squared error (MSE) of ML-VAMP can be exactly predicted in a certain large system limit (LSL) where the numbers of layers is fixed and weight matrices are random and orthogonally-invariant with dimensions that grow to infinity. ML-VAMP is thus a principled method for output-to-input inference in deep networks with a rigorous and precise performance achievability result in high dimensions.