arXiv subjects

Jonathan Baxter

Publications and source records attributed to Jonathan Baxter.

24 records · Page 2Linked to original sources

arXiv2019

Learning Model Bias

In this paper the problem of {\em learning} appropriate domain-specific bias is addressed. It is shown that this can be achieved by learning many related tasks from the same domain, and a theorem is given bounding the number tasks that must be learnt. A corollary of the theorem is that if the tasks are known to possess a common {\em internal representation} or {\em preprocessing} then the number of examples required per task for good generalisation when learning $n$ tasks simultaneously scales like $O(a + \frac{b}{n})$, where $O(a)$ is a bound on the minimum number of examples required to learn a single task, and $O(a + b)$ is a bound on the number of examples required to learn each task independently. An experiment providing strong qualitative support for the theoretical results is reported.

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arXiv2019

The Canonical Distortion Measure for Vector Quantization and Function Approximation

To measure the quality of a set of vector quantization points a means of measuring the distance between a random point and its quantization is required. Common metrics such as the {\em Hamming} and {\em Euclidean} metrics, while mathematically simple, are inappropriate for comparing natural signals such as speech or images. In this paper it is shown how an {\em environment} of functions on an input space $X$ induces a {\em canonical distortion measure} (CDM) on X. The depiction 'canonical" is justified because it is shown that optimizing the reconstruction error of X with respect to the CDM gives rise to optimal piecewise constant approximations of the functions in the environment. The CDM is calculated in closed form for several different function classes. An algorithm for training neural networks to implement the CDM is presented along with some encouraging experimental results.

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arXiv2019

A Bayesian/Information Theoretic Model of Bias Learning

In this paper the problem of learning appropriate bias for an environment of related tasks is examined from a Bayesian perspective. The environment of related tasks is shown to be naturally modelled by the concept of an {\em objective} prior distribution. Sampling from the objective prior corresponds to sampling different learning tasks from the environment. It is argued that for many common machine learning problems, although we don't know the true (objective) prior for the problem, we do have some idea of a set of possible priors to which the true prior belongs. It is shown that under these circumstances a learner can use Bayesian inference to learn the true prior by sampling from the objective prior. Bounds are given on the amount of information required to learn a task when it is simultaneously learnt with several other tasks. The bounds show that if the learner has little knowledge of the true prior, and the dimensionality of the true prior is small, then sampling multiple tasks is highly advantageous.

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arXiv2019

92c/MFlops/s, Ultra-Large-Scale Neural-Network Training on a PIII Cluster

Artificial neural networks with millions of adjustable parameters and a similar number of training examples are a potential solution for difficult, large-scale pattern recognition problems in areas such as speech and face recognition, classification of large volumes of web data, and finance. The bottleneck is that neural network training involves iterative gradient descent and is extremely computationally intensive. In this paper we present a technique for distributed training of Ultra Large Scale Neural Networks (ULSNN) on Bunyip, a Linux-based cluster of 196 Pentium III processors. To illustrate ULSNN training we describe an experiment in which a neural network with 1.73 million adjustable parameters was trained to recognize machine-printed Japanese characters from a database containing 9 million training patterns. The training runs with a average performance of 163.3 GFlops/s (single precision). With a machine cost of \$150,913, this yields a price/performance ratio of 92.4c/MFlops/s (single precision). For comparison purposes, training using double precision and the ATLAS DGEMM produces a sustained performance of 70 MFlops/s or \$2.16 / MFlop/s (double precision).

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arXiv1999

KnightCap: A chess program that learns by combining TD(lambda) with game-tree search

In this paper we present TDLeaf(lambda), a variation on the TD(lambda) algorithm that enables it to be used in conjunction with game-tree search. We present some experiments in which our chess program ``KnightCap'' used TDLeaf(lambda) to learn its evaluation function while playing on the Free Internet Chess Server (FICS, fics.onenet.net). The main success we report is that KnightCap improved from a 1650 rating to a 2150 rating in just 308 games and 3 days of play. As a reference, a rating of 1650 corresponds to about level B human play (on a scale from E (1000) to A (1800)), while 2150 is human master level. We discuss some of the reasons for this success, principle among them being the use of on-line, rather than self-play.

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arXiv1999

TDLeaf(lambda): Combining Temporal Difference Learning with Game-Tree Search

In this paper we present TDLeaf(lambda), a variation on the TD(lambda) algorithm that enables it to be used in conjunction with minimax search. We present some experiments in both chess and backgammon which demonstrate its utility and provide comparisons with TD(lambda) and another less radical variant, TD-directed(lambda). In particular, our chess program, ``KnightCap,'' used TDLeaf(lambda) to learn its evaluation function while playing on the Free Internet Chess Server (FICS, fics.onenet.net). It improved from a 1650 rating to a 2100 rating in just 308 games. We discuss some of the reasons for this success and the relationship between our results and Tesauro's results in backgammon.

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