1,823 research outputs found
How to shift bias: Lessons from the Baldwin effect
An inductive learning algorithm takes a set of data as input and generates a hypothesis as
output. A set of data is typically consistent with an infinite number of hypotheses;
therefore, there must be factors other than the data that determine the output of the
learning algorithm. In machine learning, these other factors are called the bias of the
learner. Classical learning algorithms have a fixed bias, implicit in their design. Recently
developed learning algorithms dynamically adjust their bias as they search for a
hypothesis. Algorithms that shift bias in this manner are not as well understood as
classical algorithms. In this paper, we show that the Baldwin effect has implications for
the design and analysis of bias shifting algorithms. The Baldwin effect was proposed in
1896, to explain how phenomena that might appear to require Lamarckian evolution
(inheritance of acquired characteristics) can arise from purely Darwinian evolution.
Hinton and Nowlan presented a computational model of the Baldwin effect in 1987. We
explore a variation on their model, which we constructed explicitly to illustrate the lessons
that the Baldwin effect has for research in bias shifting algorithms. The main lesson is that
it appears that a good strategy for shift of bias in a learning algorithm is to begin with a
weak bias and gradually shift to a strong bias
Explicit Learning Curves for Transduction and Application to Clustering and Compression Algorithms
Inductive learning is based on inferring a general rule from a finite data
set and using it to label new data. In transduction one attempts to solve the
problem of using a labeled training set to label a set of unlabeled points,
which are given to the learner prior to learning. Although transduction seems
at the outset to be an easier task than induction, there have not been many
provably useful algorithms for transduction. Moreover, the precise relation
between induction and transduction has not yet been determined. The main
theoretical developments related to transduction were presented by Vapnik more
than twenty years ago. One of Vapnik's basic results is a rather tight error
bound for transductive classification based on an exact computation of the
hypergeometric tail. While tight, this bound is given implicitly via a
computational routine. Our first contribution is a somewhat looser but explicit
characterization of a slightly extended PAC-Bayesian version of Vapnik's
transductive bound. This characterization is obtained using concentration
inequalities for the tail of sums of random variables obtained by sampling
without replacement. We then derive error bounds for compression schemes such
as (transductive) support vector machines and for transduction algorithms based
on clustering. The main observation used for deriving these new error bounds
and algorithms is that the unlabeled test points, which in the transductive
setting are known in advance, can be used in order to construct useful data
dependent prior distributions over the hypothesis space
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