Our central goal is to quantify the long-term progression of pediatric neurological diseases, such as a typical 10-15 years progression of child dystonia. To this purpose, quantitative models are convincing only if they can provide multi-scale details ranging from neuron spikes to limb biomechanics. The models also need to be evaluated in hyper-time, i.e. significantly faster than real-time, for producing useful predictions. We designed a platform with digital VLSI hardware for multi-scale hyper-time emulations of human motor nervous systems. The platform is constructed on a scalable, distributed array of Field Programmable Gate Array (FPGA) devices. All devices operate asynchronously with 1 millisecond time granularity, and the overall system is accelerated to 365x real-time. Each physiological component is implemented using models from well documented studies and can be flexibly modified. Thus the validity of emulation can be easily advised by neurophysiologists and clinicians. For maximizing the speed of emulation, all calculations are implemented in combinational logic instead of clocked iterative circuits. This paper presents the methodology of building FPGA modules in correspondence to components of a monosynaptic spinal loop. Results of emulated activities are shown. The paper also discusses the rationale of approximating neural circuitry by organizing neurons with sparse interconnections. In conclusion, our platform allows introducing various abnormalities into the neural emulation such that the emerging motor symptoms can be analyzed. It compels us to test the origins of childhood motor disorders and predict their long-term progressions.

We present a new formulation for attacking binary classification problems. Instead of relying on convex losses and regularisers such as in SVMs, logistic regression and boosting, or instead non-convex but continuous formulations such as those encountered in neural networks and deep belief networks, our framework entails a non-convex but \emph{discrete} formulation, where estimation amounts to finding a MAP configuration in a graphical model whose potential functions are low-dimensional discrete surrogates for the misclassification loss. We argue that such a discrete formulation can naturally account for a number of issues that are typically encountered in either the convex or the continuous non-convex paradigms, or both. By reducing the learning problem to a MAP inference problem, we can immediately translate the guarantees available for many inference settings to the learning problem itself. We empirically demonstrate in a number of experiments that this approach is promising in dealing with issues such as severe label noise, while still having global optimality guarantees. Due to the discrete nature of the formulation, it also allows for \emph{direct} regularisation through cardinality-based penalties, such as the $\ell_0$ pseudo-norm, thus providing the ability to perform feature selection and trade-off interpretability and predictability in a principled manner. We also outline a number of open problems arising from the formulation.

We study the scalability of consensus-based distributed optimization algorithms by considering two questions: How many processors should we use for a given problem, and how often should they communicate when communication is not free? Central to our analysis is a problem-specific value $r$ which quantifies the communication/computation tradeoff. We show that organizing the communication among nodes as a $k$-regular expander graph~\cite{kRegExpanders} yields speedups, while when all pairs of nodes communicate (as in a complete graph), there is an optimal number of processors that depends on $r$. Surprisingly, a speedup can be obtained, in terms of the time to reach a fixed level of accuracy, by communicating less and less frequently as the computation progresses. Experiments on a real cluster solving metric learning and non-smooth convex minimization tasks demonstrate strong agreement between theory and practice.

We describe how the pre-training algorithm for Deep Boltzmann Machines (DBMs) is related to the pre-training algorithm for Deep Belief Networks and we show that under certain conditions, the pre-training procedure improves the variational lower bound of a two-hidden-layer DBM. Based on this analysis, we develop a different method of pre-training DBMs that distributes the modelling work more evenly over the hidden layers. Our results on the MNIST and NORB datasets demonstrate that the new pre-training algorithm allows us to learn better generative models.

This paper suggests a learning-theoretic perspective on how synaptic plasticity benefits global brain functioning. We introduce a model, the selectron, that (i) arises as the fast time constant limit of leaky integrate-and-fire neurons equipped with spiking timing dependent plasticity (STDP) and (ii) is amenable to theoretical analysis. We show that the selectron encodes reward estimates into spikes and that an error bound on spikes is controlled by a spiking margin and the sum of synaptic weights. Moreover, the efficacy of spikes (their usefulness to other reward maximizing selectrons) also depends on total synaptic strength. Finally, based on our analysis, we propose a regularized version of STDP, and show the regularization improves the robustness of neuronal learning when faced with multiple stimuli.

We introduce a new discrepancy score between two distributions that gives an indication on their \emph{similarity}. While much research has been done to determine if two samples come from exactly the same distribution, much less research considered the problem of determining if two finite samples come from similar distributions. The new score gives an intuitive interpretation of similarity; it optimally perturbs the distributions so that they best fit each other. The score is defined between distributions, and can be efficiently estimated from samples. We provide convergence bounds of the estimated score, and develop hypothesis testing procedures that test if two data sets come from similar distributions. The statistical power of this procedures is presented in simulations. We also compare the score's capacity to detect similarity with that of other known measures on real data.

Numerical integration is an key component of many problems in scientific computing, statistical modelling, and machine learning. Bayesian Quadrature is a model-based method for numerical integration which, relative to standard Monte Carlo methods, offers increased sample efficiency and a more robust estimate of the uncertainty in the estimated integral. We propose a novel Bayesian Quadrature approach for numerical integration when the integrand is non-negative, such as the case of computing the marginal likelihood, predictive distribution, or normalising constant of a probabilistic model. Our approach approximately marginalises the quadrature model's hyperparameters in closed form, and introduces an active learning scheme to optimally select function evaluations, as opposed to using Monte Carlo samples. We demonstrate our method on both a number of synthetic benchmarks and a real scientific problem from astronomy.

We derive a novel norm that corresponds to the tightest convex relaxation of sparsity combined with an $\ell_2$ penalty. We show that this new norm provides a tighter relaxation than the elastic net, and is thus a good replacement for the Lasso or the elastic net in sparse prediction problems. But through studying our new norm, we also bound the looseness of the elastic net, thus shedding new light on it and providing justification for its use.

Characterizing the information carried by neural populations in the brain requires accurate statistical models of neural spike responses. The negative-binomial distribution provides a convenient model for over-dispersed spike counts, that is, responses with greater-than-Poisson variability. Here we describe a powerful data-augmentation framework for fully Bayesian inference in neural models with negative-binomial spiking. Our approach relies on a recently described latent-variable representation of the negative-binomial distribution, which equates it to a Polya-gamma mixture of normals. This framework provides a tractable, conditionally Gaussian representation of the posterior that can be used to design efficient EM and Gibbs sampling based algorithms for inference in regression and dynamic factor models. We apply the model to neural data from primate retina and show that it substantially outperforms Poisson regression on held-out data, and reveals latent structure underlying spike count correlations in simultaneously recorded spike trains.

We describe the tradeoff between the performance in a visual recognition problem and the control authority that the agent can exercise on the sensing process. We focus on the problem of "visual search" of an object in an otherwise known and static scene, propose a measure of control authority, and relate it to the expected risk and its proxy (conditional entropy of the posterior density). We show this analytically, as well as empirically by simulation using the simplest known model that captures the phenomenology of image formation, including scaling and occlusions. We show that a "passive" agent given a training set can provide no guarantees on performance beyond what is afforded by the priors, and that an "omnipotent" agent, capable of infinite control authority, can achieve arbitrarily good performance (asymptotically). In between these limiting cases, the tradeoff can be characterized empirically.