Accurate and detailed models of the progression of neurodegenerative diseases such as Alzheimer's (AD) are crucially important for reliable early diagnosis and the determination and deployment of effective treatments. In this paper, we introduce the ALPACA (Alzheimer's disease Probabilistic Cascades) model, a generative model linking latent Alzheimer's progression dynamics to observable biomarker data. In contrast with previous works which model disease progression as a fixed ordering of events, we explicitly model the variability over such orderings among patients which is more realistic, particularly for highly detailed disease progression models. We describe efficient learning algorithms for ALPACA and discuss promising experimental results on a real cohort of Alzheimer's patients from the Alzheimer's Disease Neuroimaging Initiative.

Recent experiments have demonstrated that humans and animals typically reason probabilistically about their environment. This ability requires a neural code that represents probability distributions and neural circuits that are capable of implementing the operations of probabilistic inference. The proposed probabilistic population coding (PPC) framework provides a statistically efficient neural representation of probability distributions that is both broadly consistent with physiological measurements and capable of implementing some of the basic operations of probabilistic inference in a biologically plausible way. However, these experiments and the corresponding neural models have largely focused on simple (tractable) probabilistic computations such as cue combination, coordinate transformations, and decision making. As a result it remains unclear how to generalize this framework to more complex probabilistic computations. Here we address this short coming by showing that a very general approximate inference algorithm known as Variational Bayesian Expectation Maximization can be implemented within the linear PPC framework. We apply this approach to a generic problem faced by any given layer of cortex, namely the identification of latent causes of complex mixtures of spikes. We identify a formal equivalent between this spike pattern demixing problem and topic models used for document classification, in particular Latent Dirichlet Allocation (LDA). We then construct a neural network implementation of variational inference and learning for LDA that utilizes a linear PPC. This network relies critically on two non-linear operations: divisive normalization and super-linear facilitation, both of which are ubiquitously observed in neural circuits. We also demonstrate how online learning can be achieved using a variation of Hebb’s rule and describe an extesion of this work which allows us to deal with time varying and correlated latent causes.

The human mind has a remarkable ability to store a vast amount of information in memory, and an even more remarkable ability to retrieve these experiences when needed. Understanding the representations and algorithms that underlie human memory search could potentially be useful in other information retrieval settings, including internet search. Psychological studies have revealed clear regularities in how people search their memory, with clusters of semantically related items tending to be retrieved together. These findings have recently been taken as evidence that human memory search is similar to animals foraging for food in patchy environments, with people making a rational decision to switch away from a cluster of related information as it becomes depleted. We demonstrate that the results that were taken as evidence for this account also emerge from a random walk on a semantic network, much like the random web surfer model used in internet search engines. This offers a simpler and more unified account of how people search their memory, postulating a single process rather than one process for exploring a cluster and one process for switching between clusters.

Natural sounds exhibit complex statistical regularities at multiple scales. Acoustic eventsunderlying speech, for example, are characterized by precise temporal and frequency relationships, but they can also vary substantially according to the pitch, duration, and other high-level properties of speech production. Learning this structure from data while capturing the inherent variability is an important first step in building auditory processing systems, as well as understanding the mechanisms of auditory perception. Here we develop Hierarchical Spike Coding, a two-layer probabilistic generative model for complex acoustic structure. The first layer consists of a sparse spiking representation that encodes the sound using kernelspositioned precisely in time and frequency. Patterns in the positions of first layer spikes are learned from the data: on a coarse scale, statistical regularities areencoded by a second-layer spiking representation, while fine-scale structure is captured by recurrent interactions within the first layer. When fit to speech data, the second layer acoustic features include harmonic stacks, sweeps, frequency modulations, and precise temporal onsets, which can be composed to represent complex acoustic events. Unlike spectrogram-based methods, the model gives a probability distribution over sound pressure waveforms. This allows us to use the second-layer representation to synthesize sounds directly, and to perform model-based denoising, on which we demonstrate a significant improvement over standard methods.

Factor analysis models effectively summarise the covariance structure of high dimensional data,but the solutions are typically hard to interpret. This motivates attempting to find a disjoint partition, i.e. a simple clustering, of observed variables into highly correlated subsets. We introduce a Bayesian nonparametric approach to this problem, and demonstrate advantages over heuristic methods proposed to date. Our Dirichlet process variable clustering (DPVC) model can discover blockdiagonal covariancestructures in data. We evaluate our method on both synthetic and gene expression analysis problems.

We introduce a new prior for use in Nonparametric Bayesian Hierarchical Clustering. The prior is constructed by marginalizing out the time information of Kingman’s coalescent, providing a prior over tree structures which we call the Time-Marginalized Coalescent (TMC). This allows for models which factorize the tree structure and times, providing two benefits: more flexible priors may be constructed and more efficient Gibbs type inference can be used. We demonstrate this on an example model for density estimation and show the TMC achieves competitive experimental results.

Sparse learning models typically combine a smooth loss with a nonsmooth penalty, such as trace norm. Although recent developments in sparse approximation have offered promising solution methods, current approaches either apply only to matrix-norm constrained problems or provide suboptimal convergence rates. In this paper, we propose a boosting method for regularized learning that guarantees $\epsilon$ accuracy within $O(1/\epsilon)$ iterations. Performance is further accelerated by interlacing boosting with fixed-rank local optimization---exploiting a simpler local objective than previous work. The proposed method yields state-of-the-art performance on large-scale problems. We also demonstrate an application to latent multiview learning for which we provide the first efficient weak-oracle.

Pedigrees, or family trees, are directed graphs used to identify sites of the genome that are correlated with the presence or absence of a disease. With the advent of genotyping and sequencing technologies, there has been an explosion in the amount of data available, both in the number of individuals and in the number of sites. Some pedigrees number in the thousands of individuals. Meanwhile, analysis methods have remained limited to pedigrees of <100 individuals which limits analyses to many small independent pedigrees. Disease models, such those used for the linkage analysis log-odds (LOD) estimator, have similarly been limited. This is because linkage anlysis was originally designed with a different task in mind, that of ordering the sites in the genome, before there were technologies that could reveal the order. LODs are difficult to interpret and nontrivial to extend to consider interactions among sites. These developments and difficulties call for the creation of modern methods of pedigree analysis. Drawing from recent advances in graphical model inference and transducer theory, we introduce a simple yet powerful formalism for expressing genetic disease models. We show that these disease models can be turned into accurate and efficient estimators. The technique we use for constructing the variational approximation has potential applications to inference in other large-scale graphical models. This method allows inference on larger pedigrees than previously analyzed in the literature, which improves disease site prediction.

We present a Bayesian nonparametric model for genetic sequence data in which a set of genetic sequences is modelled using a Markov model of partitions. The partitions at consecutive locations in the genome are related by their clusters first splitting and then merging. Our model can be thought of as a discrete time analogue of continuous time fragmentation-coagulation processes [Teh et al 2011], preserving the important properties of projectivity, exchangeability and reversibility, while being more scalable. We apply this model to the problem of genotype imputation, showing improved computational efficiency while maintaining the same accuracies as in [Teh et al 2011].

We address a central problem of neuroanatomy, namely, the automatic segmentation of neuronal structures depicted in stacks of electron microscopy (EM) images. This is necessary to efficiently map 3D brain structure and connectivity. To segment {\em biological} neuron membranes, we use a special type of deep {\em artificial} neural network as a pixel classifier. The label of each pixel (membrane or non-membrane) is predicted from raw pixel values in a square window centered on it. The input layer maps each window pixel to a neuron. It is followed by a succession of convolutional and max-pooling layers which preserve 2D information and extract features with increasing levels of abstraction. The output layer produces a calibrated probability for each class. The classifier is trained by plain gradient descent on a $512 \times 512 \times 30$ stack with known ground truth, and tested on a stack of the same size (ground truth unknown to the authors) by the organizers of the ISBI 2012 EM Segmentation Challenge. Even without problem-specific post-processing, our approach outperforms competing techniques by a large margin in all three considered metrics, i.e. \emph{rand error}, \emph{warping error} and \emph{pixel error}. For pixel error, our approach is the only one outperforming a second human observer.