Learning dynamic models from observed data has been a central issue in many scientific studies or engineering tasks. The usual setting is that data are collected sequentially from trajectories of some dynamical system operation. In quite a few modern scientific modeling tasks, however, it turns out that reliable sequential data are rather difficult to gather, whereas out-of-order snapshots are much easier to obtain. Examples include the modeling of galaxies, chronic diseases such Alzheimer's, or certain biological processes. Existing methods for learning dynamic model from non-sequence data are mostly based on Expectation-Maximization, which involves non-convex optimization and is thus hard to analyze. Inspired by recent advances in spectral learning methods, we propose to study this problem from a different perspective: moment matching and spectral decomposition. Under that framework, we identify reasonable assumptions on the generative process of non-sequence data, and propose learning algorithms based on the tensor decomposition method \cite{anandkumar2012tensor} to \textit{provably} recover first-order Markov models and hidden Markov models. To the best of our knowledge, this is the first formal guarantee on learning from non-sequence data. Preliminary simulation results confirm our theoretical findings.

With simultaneous measurements from ever increasing populations of neurons, there is a growing need for sophisticated tools to recover signals from individual neurons. In electrophysiology experiments, this classically proceeds in a two-step process: (i) threshold the waveforms to detect putative spikes and (ii) cluster the waveforms into single units (neurons). We extend previous Bayesian nonparamet- ric models of neural spiking to jointly detect and cluster neurons using a Gamma process model. Importantly, we develop an online approximate inference scheme enabling real-time analysis, with performance exceeding the previous state-of-the- art. Via exploratory data analysis—using data with partial ground truth as well as two novel data sets—we find several features of our model collectively contribute to our improved performance including: (i) accounting for colored noise, (ii) de- tecting overlapping spikes, (iii) tracking waveform dynamics, and (iv) using mul- tiple channels. We hope to enable novel experiments simultaneously measuring many thousands of neurons and possibly adapting stimuli dynamically to probe ever deeper into the mysteries of the brain.

Natural actor-critics are a popular class of policy search algorithms for finding locally optimal policies for Markov decision processes. In this paper we address a drawback of natural actor-critics that limits their real-world applicability - their lack of safety guarantees. We present a principled algorithm for performing natural gradient descent over a constrained domain. In the context of reinforcement learning, this allows for natural actor-critic algorithms that are guaranteed to remain within a known safe region of policy space. While deriving our class of constrained natural actor-critic algorithms, which we call Projected Natural Actor-Critics (PNACs), we also elucidate the relationship between natural gradient descent and mirror descent.

A common problem in knowledge representation and related fields is reasoning over a large joint knowledge graph, represented as triples of a relation between two entities. The goal of this paper is to develop a more powerful neural network model suitable for inference over these relationships. Previous models suffer from weak interaction between entities or simple linear projection of the vector space. We address these problems by introducing a neural tensor network (NTN) model which allow the entities and relations to interact multiplicatively. Additionally, we observe that such knowledge base models can be further improved by representing each entity as the average of vectors for the words in the entity name, giving an additional dimension of similarity by which entities can share statistical strength. We assess the model by considering the problem of predicting additional true relations between entities given a partial knowledge base. Our model outperforms previous models and can classify unseen relationships in WordNet and FreeBase with an accuracy of 86.2% and 90.0%, respectively.

Motivated by an application in computational biology, we consider constrained low-rank matrix factorization problems with $\{0,1\}$-constraints on one of the factors. In addition to the the non-convexity shared with more general matrix factorization schemes, our problem is further complicated by a combinatorial constraint set of size $2^{m \cdot r}$, where $m$ is the dimension of the data points and $r$ the rank of the factorization. Despite apparent intractability, we provide $-$in the line of recent work on non-negative matrix factorization by Arora et al.~(2012)$-$ an algorithm that provably recovers the underlying factorization in the exact case with operations of the order $O(m r 2^r + mnr)$ in the worst case. To obtain that result, we invoke theory centered around a fundamental result in combinatorics, the Littlewood-Offord lemma.

The adaptive anonymity problem is formalized where each individual shares their data along with an integer value to indicate their personal level of desired privacy. This problem leads to a generalization of $k$-anonymity to the $b$-matching setting. Novel algorithms and theory are provided to implement this type of anonymity. The relaxation achieves better utility, admits theoretical privacy guarantees that are as strong, and, most importantly, accommodates a variable level of anonymity for each individual. Empirical results confirm improved utility on benchmark and social data-sets.

We investigate a spiking neuron model of multisensory integration. Multiple stimuli from different sensory modalities are encoded by a single neural circuit comprised of a multisensory bank of receptive fields in cascade with a population of biophysical spike generators. We demonstrate that stimuli of different dimensions can be faithfully multiplexed and encoded in the spike domain and derive tractable algorithms for decoding each stimulus from the common pool of spikes. We also show that the identification of multisensory processing in a single neuron is dual to the recovery of stimuli encoded with a population of multisensory neurons, and prove that only a projection of the circuit onto input stimuli can be identified. We provide an example of multisensory integration using natural audio and video and discuss the performance of the proposed decoding and identification algorithms.

Population neural recordings with long-range temporal structure are often best understood in terms of a shared underlying low-dimensional dynamical process. Advances in recording technology provide access to an ever larger fraction of the population, but the standard computational approaches available to identify the collective dynamics scale poorly with the size of the dataset. Here we describe a new, scalable approach to discovering the low-dimensional dynamics that underlie simultaneously recorded spike trains from a neural population. Our method is based on recurrent linear models (RLMs), and relates closely to timeseries models based on recurrent neural networks. We formulate RLMs for neural data by generalising the Kalman-filter-based likelihood calculation for latent linear dynamical systems (LDS) models to incorporate a generalised-linear observation process. We show that RLMs describe motor-cortical population data better than either directly-coupled generalised-linear models or latent linear dynamical system models with generalised-linear observations. We also introduce the cascaded linear model (CLM) to capture low-dimensional instantaneous correlations in neural populations. The CLM describes the cortical recordings better than either Ising or Gaussian models and, like the RLM, can be fit exactly and quickly. The CLM can also be seen as a generalization of a low-rank Gaussian model, in this case factor analysis. The computational tractability of the RLM and CLM allow both to scale to very high-dimensional neural data.

Humans recognize visually-presented objects rapidly and accurately. To understand this ability, we seek to construct models of the ventral stream, the series of cortical areas thought to subserve object recognition. One tool to assess the quality of a model of the ventral stream is the Representation Dissimilarity Matrix (RDM), which uses a set of visual stimuli and measures the distances produced in either the brain (i.e. fMRI voxel responses, neural firing rates) or in models (features). Previous work has shown that all known models of the ventral stream fail to capture the RDM pattern observed in either IT cortex, the highest ventral area, or in the human ventral stream. In this work, we construct models of the ventral stream using a novel optimization procedure for category-level object recognition problems, and produce RDMs resembling both macaque IT and human ventral stream. The model, while novel in the optimization procedure, further develops a long-standing functional hypothesis that the ventral visual stream is a hierarchically arranged series of processing stages optimized for visual object recognition.

The recently introduced continuous Skip-gram model is an efficient method for learning high-quality distributed vector representations that capture a large number of precise syntactic and semantic word relationships. In this paper we present several improvements that make the Skip-gram model more expressive and enable it to learn higher quality vectors more rapidly. We show that by subsampling frequent words we obtain significant speedup, and also learn higher quality representations as measured by our tasks. We also introduce Negative Sampling, a simplified variant of Noise Contrastive Estimation (NCE) that learns more accurate vectors for frequent words compared to the hierarchical softmax. An inherent limitation of word representations is their indifference to word order and their inability to represent idiomatic phrases. For example, the meanings of Canada'' and "Air'' cannot be easily combined to obtain "Air Canada''. Motivated by this example, we present a simple and efficient method for finding phrases, and show that their vector representations can be accurately learned by the Skip-gram model. "