Gavin Brown

A typical machine learning development cycle maximizes performance during model training and then minimizes the memory and area footprint of the trained model for deployment on processing cores, graphics processing units, microcontrollers or custom hardware accelerators. However, this becomes increasingly difficult as machine learning models grow larger and more complex. Here we report a methodology for automatically generating predictor circuits for the classification of tabular data. The approach offers comparable prediction performance to conventional machine learning techniques as substantially fewer hardware resources and power are used. We use an evolutionary algorithm to search over the space of logic gates and automatically generate a classifier circuit with maximized training prediction accuracy, which consists of no more than 300 logic gates. When simulated as a silicon chip, our tiny classifiers use 8–18 times less area and 4–8 times less power than the best-performing machine learning baseline. When implemented as a low-cost chip on a flexible substrate, they occupy 10–75 times less area, consume 13–75 times less power and have 6 times better yield than the most hardware-efficient ML baseline.

We present a theory of ensemble diversity, explaining the nature of diversity for a wide range of supervised learning scenarios. This challenge has been referred to as the holy grail of ensemble learning, an open research issue for over 30 years. Our framework reveals that diversity is in fact a hidden dimension in the bias-variance decomposition of the ensemble loss. We prove a family of exact bias-variance-diversity decompositions, for a wide range of losses in both regression and classification, e.g., squared, cross-entropy, and Poisson losses. For losses where an additive bias-variance decomposition is not available (e.g., 0/1 loss) we present an alternative approach: quantifying the effects of diversity, which turn out to be dependent on the label distribution. Overall, we argue that diversity is a measure of model fit, in precisely the same sense as bias and variance, but accounting for statistical dependencies between ensemble members. Thus, we should not be maximising diversity as so many works aim to do -- instead, we have a bias/variance/diversity trade-off to manage.

This paper demonstrates how to construct ensembles of spiking neural networks producing state-of-the-art results, achieving classification accuracies of 98.71%, 100.0%, and 99.09%, on the MNIST, NMNIST and DVS Gesture datasets respectively. Furthermore, this performance is achieved using simplified individual models, with ensembles containing less than 50% of the parameters of published reference models. We provide comprehensive exploration on the effect of spike train interpretation methods, and derive the theoretical methodology for combining model predictions such that performance improvements are guaranteed for spiking ensembles. For this, we formalize spiking neural networks as GLM predictors, identifying a suitable representation for their target domain. Further, we show how the diversity of our spiking ensembles can be measured using the Ambiguity Decomposition. The work demonstrates how ensembling can overcome the challenges of producing individual SNN models which can compete with traditional deep neural networks, and creates systems with fewer trainable parameters and smaller memory footprints, opening the door to low-power edge applications, e.g. implemented on neuromorphic hardware.

The ultimate goal of a supervised learning algorithm is to produce models constructed on the training data that can generalize well to new examples. In classification, functional margin maximization -- correctly classifying as many training examples as possible with maximal confidence --has been known to construct models with good generalization guarantees. This work gives an information-theoretic interpretation of a margin maximizing model on a noiseless training dataset as one that achieves lossless maximal compression of said dataset -- i.e. extracts from the features all the useful information for predicting the label and no more. The connection offers new insights on generalization in supervised machine learning, showing margin maximization as a special case (that of classification) of a more general principle and explains the success and potential limitations of popular learning algorithms like gradient boosting. We support our observations with theoretical arguments and empirical evidence and identify interesting directions for future work.

Probability estimates generated by boosting ensembles are poorly calibrated because of the margin maximization nature of the algorithm. The outputs of the ensemble need to be properly calibrated before they can be used as probability estimates. In this work, we demonstrate that online boosting is also prone to producing distorted probability estimates. In batch learning, calibration is achieved by reserving part of the training data for training the calibrator function. In the online setting, a decision needs to be made on each round: shall the new example(s) be used to update the parameters of the ensemble or those of the calibrator. We proceed to resolve this decision with the aid of bandit optimization algorithms. We demonstrate superior performance to uncalibrated and naively-calibrated on-line boosting ensembles in terms of probability estimation. Our proposed mechanism can be easily adapted to other tasks(e.g. cost-sensitive classification) and is robust to the choice of hyperparameters of both the calibrator and the ensemble.