We describe a graph-based semi-supervised learning framework in the context of deep neural networks that uses a graph-based entropic regularizer to favor smooth solutions over a graph induced by the data. The main contribution of this work is a computationally efficient, stochastic graph-regularization technique that uses mini-batches that are consistent with the graph structure, but also provides enough stochasticity (in terms of mini-batch data diversity) for convergence of stochastic gradient descent methods to good solutions. For this work, we focus on results of frame-level phone classification accuracy on the TIMIT speech corpus but our method is general and scalable to much larger data sets. Results indicate that our method significantly improves classification accuracy compared to the fully-supervised case when the fraction of labeled data is low, and it is competitive with other methods in the fully labeled case.

The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetries of the image domain. In comparison, there are a number of problems in which there are a number of different inputs which are all 'of the same type' --- multiple particles, multiple agents, multiple stock prices, etc. The corresponding symmetry to this is permutation symmetry, in that the algorithm should not depend on the specific ordering of the input data. We discuss a permutation-invariant neural network layer in analogy to convolutional layers, and show the ability of this architecture to learn to predict the motion of a variable number of interacting hard discs in 2D. In the same way that convolutional layers can generalize to different image sizes, the permutation layer we describe generalizes to different numbers of objects.

A dynamic Boltzmann machine (DyBM) has been proposed as a model of a spiking neural network, and its learning rule of maximizing the log-likelihood of given time-series has been shown to exhibit key properties of spike-timing dependent plasticity (STDP), which had been postulated and experimentally confirmed in the field of neuroscience as a learning rule that refines the Hebbian rule. Here, we relax some of the constraints in the DyBM in a way that it becomes more suitable for computation and learning. We show that learning the DyBM can be considered as logistic regression for binary-valued time-series. We also show how the DyBM can learn real-valued data in the form of a Gaussian DyBM and discuss its relation to the vector autoregressive (VAR) model. The Gaussian DyBM extends the VAR by using additional explanatory variables, which correspond to the eligibility traces of the DyBM and capture long term dependency of the time-series. Numerical experiments show that the Gaussian DyBM significantly improves the predictive accuracy over VAR.

We present a machine learning approach to the inversion of Fredholm integrals of the first kind. The approach provides a natural regularization in cases where the inverse of the Fredholm kernel is ill-conditioned. It also provides an efficient and stable treatment of constraints. The key observation is that the stability of the forward problem permits the construction of a large database of outputs for physically meaningful inputs. We apply machine learning to this database to generate a regression function of controlled complexity, which returns approximate solutions for previously unseen inputs; the approximate solutions are then projected onto the subspace of functions satisfying relevant constraints. We also derive and present uncertainty estimates. We illustrate the approach by applying it to the analytical continuation problem of quantum many-body physics, which involves reconstructing the frequency dependence of physical excitation spectra from data obtained at specific points in the complex frequency plane. Under standard error metrics the method performs as well or better than the Maximum Entropy method for low input noise and is substantially more robust to increased input noise. We expect the methodology to be similarly effective for any problem involving a formally ill-conditioned inversion, provided that the forward problem can be efficiently solved.

Objective: The advent of Electronic Medical Records (EMR) with large electronic imaging databases along with advances in deep neural networks with machine learning has provided a unique opportunity to achieve milestones in automated image analysis. Optical coherence tomography (OCT) is the most commonly obtained imaging modality in ophthalmology and represents a dense and rich dataset when combined with labels derived from the EMR. We sought to determine if deep learning could be utilized to distinguish normal OCT images from images from patients with Age-related Macular Degeneration (AMD). Methods: Automated extraction of an OCT imaging database was performed and linked to clinical endpoints from the EMR. OCT macula scans were obtained by Heidelberg Spectralis, and each OCT scan was linked to EMR clinical endpoints extracted from EPIC. The central 11 images were selected from each OCT scan of two cohorts of patients: normal and AMD. Cross-validation was performed using a random subset of patients. Area under receiver operator curves (auROC) were constructed at an independent image level, macular OCT level, and patient level. Results: Of an extraction of 2.6 million OCT images linked to clinical datapoints from the EMR, 52,690 normal and 48,312 AMD macular OCT images were selected. A deep neural network was trained to categorize images as either normal or AMD. At the image level, we achieved an auROC of 92.78% with an accuracy of 87.63%. At the macula level, we achieved an auROC of 93.83% with an accuracy of 88.98%. At a patient level, we achieved an auROC of 97.45% with an accuracy of 93.45%. Peak sensitivity and specificity with optimal cutoffs were 92.64% and 93.69% respectively. Conclusions: Deep learning techniques are effective for classifying OCT images. These findings have important implications in utilizing OCT in automated screening and computer aided diagnosis tools.

Spectral analysis of neighborhood graphs is one of the most widely used techniques for exploratory data analysis, with applications ranging from machine learning to social sciences. In such applications, it is typical to first encode relationships between the data samples using an appropriate similarity function. Popular neighborhood construction techniques such as k-nearest neighbor (k-NN) graphs are known to be very sensitive to the choice of parameters, and more importantly susceptible to noise and varying densities. In this paper, we propose the use of quantile analysis to obtain local scale estimates for neighborhood graph construction. To this end, we build an auto-encoding neural network approach for inferring conditional quantiles of a similarity function, which are subsequently used to obtain robust estimates of the local scales. In addition to being highly resilient to noise or outlying data, the proposed approach does not require extensive parameter tuning unlike several existing methods. Using applications in spectral clustering and single-example label propagation, we show that the proposed neighborhood graphs outperform existing locally scaled graph construction approaches.

A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric. Learning such a metric is a hot topic since more than ten years now, and a number of methods have been proposed to efficiently learn it. However, the nature of the problem makes it quite difficult for large scale data, as well as data for which classes overlap. This paper presents a simple way of improving accuracy and scalability of any iterative metric learning algorithm, where constraints are obtained prior to the algorithm. The proposed approach relies on a loss-dependent weighted selection of constraints that are used for learning the metric. Using the corresponding dedicated loss function, the method clearly allows to obtain better results than state-of-the-art methods, both in terms of accuracy and time complexity. Some experimental results on real world, and potentially large, datasets are demonstrating the effectiveness of our proposition.

Learning from the crowd has become increasingly popular in the Web and social media. There is a wide variety of crowdlearning sites in which, on the one hand, users learn from the knowledge that other users contribute to the site, and, on the other hand, knowledge is reviewed and curated by the same users using assessment measures such as upvotes or likes. In this paper, we present a probabilistic modeling framework of crowdlearning, which uncovers the evolution of a user's expertise over time by leveraging other users' assessments of her contributions. The model allows for both off-site and on-site learning and captures forgetting of knowledge. We then develop a scalable estimation method to fit the model parameters from millions of recorded learning and contributing events. We show the effectiveness of our model by tracing activity of ~25 thousand users in Stack Overflow over a 4.5 year period. We find that answers with high knowledge value are rare. Newbies and experts tend to acquire less knowledge than users in the middle range. Prolific learners tend to be also proficient contributors that post answers with high knowledge value.

Quantum annealing is a generic solver of the optimization problem that uses fictitious quantum fluctuation. Its simulation in classical computing is often performed using the quantum Monte Carlo simulation via the Suzuki--Trotter decomposition. However, the negative sign problem sometimes emerges in the simulation of quantum annealing with an elaborate driver Hamiltonian, since it belongs to a class of non-stoquastic Hamiltonians. In the present study, we propose an alternative way to avoid the negative sign problem involved in a particular class of the non-stoquastic Hamiltonians. To check the validity of the method, we demonstrate our method by applying it to a simple problem that includes the anti-ferromagnetic XX interaction, which is a typical instance of the non-stoquastic Hamiltonians.

Many data-driven approaches exist to extract neural representations of functional magnetic resonance imaging (fMRI) data, but most of them lack a proper probabilistic formulation. We propose a group level scalable probabilistic sparse factor analysis (psFA) allowing spatially sparse maps, component pruning using automatic relevance determination (ARD) and subject specific heteroscedastic spatial noise modeling. For task-based and resting state fMRI, we show that the sparsity constraint gives rise to components similar to those obtained by group independent component analysis. The noise modeling shows that noise is reduced in areas typically associated with activation by the experimental design. The psFA model identifies sparse components and the probabilistic setting provides a natural way to handle parameter uncertainties. The variational Bayesian framework easily extends to more complex noise models than the presently considered.