Repeating patterns of precisely timed activity across a group of neurons (called frequent episodes) are indicative of networks in the underlying neural tissue. This letter develops statistical methods to determine functional connectivity among neurons based on nonoverlapping occurrences of episodes. We study the distribution of episode counts and develop a two-phase strategy for identifying functional connections. For the first phase, we develop statistical procedures that are used to screen all two-node episodes and identify possible functional connections (edges). For the second phase, we develop additional statistical procedures to prune the two-node episodes and remove false edges that can be attributed to chains or fan-out structures. The restriction to nonoverlapping occurrences makes the counting of all two-node episodes in phase 1 computationally efficient. The second (pruning) phase is critical since phase 1 can yield a large number of false connections. The scalability of the two-phase approach is examined through simulation. The method is then used to reconstruct the graph structure of observed neuronal networks, first from simulated data and then from recordings of cultured cortical neurons.

We consider the problem of detecting statistically significant sequential patterns in multineuronal spike trains. These patterns are characterized by ordered sequences of spikes from different neurons with specific delays between spikes. We have previously proposed a data-mining scheme to efficiently discover such patterns, which occur often enough in the data. Here we propose a method to determine the statistical significance of such repeating patterns. The novelty of our approach is that we use a compound null hypothesis that not only includes models of independent neurons but also models where neurons have weak dependencies. The strength of interaction among the neurons is represented in terms of certain pair-wise conditional probabilities. We specify our null hypothesis by putting an upper bound on all such conditional probabilities. We construct a probabilistic model that captures the counting process and use this to derive a test of significance for rejecting such a compound null hypothesis. The structure of our null hypothesis also allows us to rank-order different significant patterns. We illustrate the effectiveness of our approach using spike trains generated with a simulator.

Frequent episode discovery is a popular framework for mining data available as a long sequence of events. An episode is essentially a short ordered sequence of event types and the frequency of an episode is some suitable measure of how often the episode occurs in the data sequence. Recently,we proposed a new frequency measure for episodes based on the notion of non-overlapped occurrences of episodes in the event sequence, and showed that, such a definition, in addition to yielding computationally efficient algorithms, has some important theoretical properties in connecting frequent episode discovery with HMM learning. This paper presents some new algorithms for frequent episode discovery under this non-overlapped occurrences-based frequency definition. The algorithms presented here are better (by a factor of N, where N denotes the size of episodes being discovered) in terms of both time and space complexities when compared to existing methods for frequent episode discovery. We show through some simulation experiments, that our algorithms are very efficient. The new algorithms presented here have arguably the least possible orders of spaceand time complexities for the task of frequent episode discovery.

This paper is concerned with the framework of frequent episode discovery in event sequences. A new temporal pattern, called the generalized episode, is defined, which extends this framework by incorporating event duration constraints explicitly into the pattern's definition. This new formalism facilitates extension of the technique of episodes discovery to applications where data appears as a sequence of events that persist for different durations (rather than being instantaneous). We present efficient algorithms for episode discovery in this new framework. Through extensive simulations, we show the expressive power of the new formalism. We also show how the duration constraint possibilities can be used as a design choice to properly focus the episode discovery process. Finally, we briefly discuss some interesting results obtained on data from manufacturing plants of General Motors.

This paper establishes a formal connection between two common, but previously unconnected methods for analyzing data streams: discovering frequent episodes in a computer science framework and learning generative models in a statistics framework. We introduce a special class of discrete hidden Markov models (HMMs), called episode generating HMMs (EGHs), and associate each episode with a unique EGH. We prove that, given any two episodes, the EGH that is more likely to generate a given data sequence is the one associated with the more frequent episode. To be able to establish such a relationship, we define a new measure of frequency of an episode, based on what we call nonoverlapping occurrences of the episode in the data. An efficient algorithm is proposed for counting the frequencies for a set of episodes. Through extensive simulations, we show that our algorithm is both effective and more efficient than current methods for frequent episode discovery. We also show how the association between frequent episodes and EGHs can be exploited to assess the significance of frequent episodes discovered and illustrate empirically how this idea may be used to improve the efficiency of the frequent episode discovery.

Alopex is a correlation-based gradient-free optimization technique useful in many learning problems. However, there are no analytical results on the asymptotic behavior of this algorithm. This article presents a new version of Alopex that can be analyzed using techniques of two timescale stochastic approximation method. It is shown that the algorithm asymptotically behaves like a gradient-descent method, though it does not need (or estimate) any gradient information. It is also shown, through simulations, that the algorithm is quite effective.

We present a learning algorithm for neural networks, called Alopex. Instead of error gradient, Alopex uses local correlations between changes in individual weights and changes in the global error measure. The algorithm does not make any assumptions about transfer functions of individual neurons, and does not explicitly depend on the functional form of the error measure. Hence, it can be used in networks with arbitrary transfer functions and for minimizing a large class of error measures. The learning algorithm is the same for feedforward and recurrent networks. All the weights in a network are updated simultaneously, using only local computations. This allows complete parallelization of the algorithm. The algorithm is stochastic and it uses a “temperature” parameter in a manner similar to that in simulated annealing. A heuristic “annealing schedule” is presented that is effective in finding global minima of error surfaces. In this paper, we report extensive simulation studies illustrating these advantages and show that learning times are comparable to those for standard gradient descent methods. Feedforward networks trained with Alopex are used to solve the MONK's problems and symmetry problems. Recurrent networks trained with the same algorithm are used for solving temporal XOR problems. Scaling properties of the algorithm are demonstrated using encoder problems of different sizes and advantages of appropriate error measures are illustrated using a variety of problems.

This paper discusses memory neuron networks as models for identification and adaptive control of nonlinear dynamical systems. These are a class of recurrent networks obtained by adding trainable temporal elements to feedforward networks that makes the output history-sensitive. By virtue of this capability, these networks can identify dynamical systems without having to be explicitly fed with past inputs and outputs. Thus, they can identify systems whose order is unknown or systems with unknown delay. It is argued that for satisfactory modeling of dynamical systems, neural networks should be endowed with such internal memory. The paper presents a preliminary analysis of the learning algorithm, providing theoretical justification for the identification method. Methods for adaptive control of nonlinear systems using these networks are presented. Through extensive simulations, these models are shown to be effective both for identification and model reference adaptive control of nonlinear systems.

Neural networks with time delays have been used successfully for speech recognition, but most of these networks have fixed delays and a training algorithm is used only for learning the pattern of connections. A learning algorithm that can also be used to train the characteristics of time delays is introduced. The learning algorithm minimizes a mutual discrimination error measure. Networks where the connection strengths and delay parameters are learned can be used to recognize temporal patterns (words) of arbitrary lengths. The feasibility of this algorithm is shown on a network that has been used previously with fixed delays for digit recognition. Improvement in recognition accuracy due to training the delay characteristics is demonstrated using a multispeaker digit database.>

The capability of a small neural network to perform speaker-independent recognition of spoken digits in connected speech has been investigated. The network uses time delays to organize rapidly changing outputs of symbol detectors over the time scale of a word. The network is data driven and unclocked. To achieve useful accuracy in a speaker-independent setting, many new ideas and procedures were developed. These include improving the feature detectors, self-recognition of word ends, reduction in network size, and dividing speakers into natural classes. Quantitative experiments based on Texas Instruments (TI) digit databases are described.