[Paper Review] Learning binary or real-valued time-series via spike-timing dependent plasticity

Takayuki Osogami|arXiv (Cornell University)|Dec 15, 2016

Advanced Memory and Neural Computing16 references3 citations

TL;DR

This paper extends the Dynamic Boltzmann Machine (DyBM) to learn both binary and real-valued time-series by relaxing prior constraints, enabling it to function as logistic regression for binary data and as a Gaussian DyBM for real-valued data. The Gaussian DyBM improves predictive accuracy over VAR models by incorporating synaptic eligibility traces that capture long-term dependencies, reducing prediction error by up to 20% with comparable computational cost.

ABSTRACT

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.

Motivation & Objective

• To generalize the Dynamic Boltzmann Machine (DyBM) by relaxing constraints that limited its computational flexibility and applicability.
• To show that the DyBM can be interpreted as logistic regression for binary-valued time-series, enabling efficient learning of spike patterns.
• To develop a Gaussian DyBM for real-valued time-series that extends the vector autoregressive (VAR) model by incorporating eligibility traces to model long-term dependencies.
• To demonstrate that the Gaussian DyBM achieves significantly better predictive performance than VAR while maintaining low computational complexity.
• To enable online, distributed, and natural gradient-based learning in the Gaussian DyBM for scalable time-series modeling.

Proposed method

• Relaxes DyBM constraints to allow a matrix-vector formulation of the energy function, enabling interpretation as logistic regression for binary time-series.
• Introduces a Gaussian DyBM model that uses a multivariate Gaussian distribution to model real-valued time-series, with parameters learned via maximum log-likelihood.
• Incorporates synaptic eligibility traces as additional explanatory variables in the prediction model, where the trace evolves as a decaying sum of past spikes.
• Uses a natural gradient update rule with AdaGrad adaptation for online learning, updating parameters and internal states (eligibility traces, FIFO queues) at each time step.
• Models the conditional mean of the time-series as a linear combination of past inputs and eligibility traces, with the eligibility trace capturing long-term dependencies via a geometric decay.
• Derives the Gaussian DyBM as a generalization of VAR, where the lag-d variable is replaced by a decayed sum of past spikes (the eligibility trace), with the special case reducing to VAR when the decay rate μ=0.

Experimental results

Research questions

• RQ1 Can the DyBM be generalized to allow more flexible computation while preserving its biological plausibility via STDP?
• RQ2 How can the DyBM be adapted to model real-valued time-series, and what is its relationship to classical time-series models like VAR?
• RQ3 To what extent do eligibility traces in the Gaussian DyBM improve predictive accuracy compared to standard VAR models?
• RQ4 Can the Gaussian DyBM be trained efficiently in an online and distributed manner without sacrificing performance?
• RQ5 What is the computational cost of incorporating eligibility traces, and does it scale favorably with time-series length and conduction delay?

Key findings

• The Gaussian DyBM reduces predictive mean squared error by up to 20% compared to the corresponding VAR model, with the improvement arising solely from the use of eligibility traces to model long-term dependencies.
• The Gaussian DyBM maintains computational complexity equivalent to VAR when using a single decay rate, with learning time growing linearly with conduction delay d.
• The model performs well even with short conduction delay (d=1), outperforming VAR with d=16, demonstrating the effectiveness of eligibility traces in capturing extended temporal context.
• Eligibility traces allow the Gaussian DyBM to model long-term dependencies beyond the fixed lag structure of VAR, enabling better generalization on time-series with complex temporal dynamics.
• The Gaussian DyBM can be trained online using stochastic gradient descent with natural gradients and AdaGrad learning rate adaptation, ensuring stable and efficient parameter updates.
• The Gaussian DyBM is computationally efficient in distributed settings, as each parameter update depends only on locally available information, enabling scalable learning.