6,404 research outputs found
A review of domain adaptation without target labels
Domain adaptation has become a prominent problem setting in machine learning
and related fields. This review asks the question: how can a classifier learn
from a source domain and generalize to a target domain? We present a
categorization of approaches, divided into, what we refer to as, sample-based,
feature-based and inference-based methods. Sample-based methods focus on
weighting individual observations during training based on their importance to
the target domain. Feature-based methods revolve around on mapping, projecting
and representing features such that a source classifier performs well on the
target domain and inference-based methods incorporate adaptation into the
parameter estimation procedure, for instance through constraints on the
optimization procedure. Additionally, we review a number of conditions that
allow for formulating bounds on the cross-domain generalization error. Our
categorization highlights recurring ideas and raises questions important to
further research.Comment: 20 pages, 5 figure
Discriminative Density-ratio Estimation
The covariate shift is a challenging problem in supervised learning that
results from the discrepancy between the training and test distributions. An
effective approach which recently drew a considerable attention in the research
community is to reweight the training samples to minimize that discrepancy. In
specific, many methods are based on developing Density-ratio (DR) estimation
techniques that apply to both regression and classification problems. Although
these methods work well for regression problems, their performance on
classification problems is not satisfactory. This is due to a key observation
that these methods focus on matching the sample marginal distributions without
paying attention to preserving the separation between classes in the reweighted
space. In this paper, we propose a novel method for Discriminative
Density-ratio (DDR) estimation that addresses the aforementioned problem and
aims at estimating the density-ratio of joint distributions in a class-wise
manner. The proposed algorithm is an iterative procedure that alternates
between estimating the class information for the test data and estimating new
density ratio for each class. To incorporate the estimated class information of
the test data, a soft matching technique is proposed. In addition, we employ an
effective criterion which adopts mutual information as an indicator to stop the
iterative procedure while resulting in a decision boundary that lies in a
sparse region. Experiments on synthetic and benchmark datasets demonstrate the
superiority of the proposed method in terms of both accuracy and robustness
Inverse Density as an Inverse Problem: The Fredholm Equation Approach
In this paper we address the problem of estimating the ratio
where is a density function and is another density, or, more generally
an arbitrary function. Knowing or approximating this ratio is needed in various
problems of inference and integration, in particular, when one needs to average
a function with respect to one probability distribution, given a sample from
another. It is often referred as {\it importance sampling} in statistical
inference and is also closely related to the problem of {\it covariate shift}
in transfer learning as well as to various MCMC methods. It may also be useful
for separating the underlying geometry of a space, say a manifold, from the
density function defined on it.
Our approach is based on reformulating the problem of estimating
as an inverse problem in terms of an integral operator
corresponding to a kernel, and thus reducing it to an integral equation, known
as the Fredholm problem of the first kind. This formulation, combined with the
techniques of regularization and kernel methods, leads to a principled
kernel-based framework for constructing algorithms and for analyzing them
theoretically.
The resulting family of algorithms (FIRE, for Fredholm Inverse Regularized
Estimator) is flexible, simple and easy to implement.
We provide detailed theoretical analysis including concentration bounds and
convergence rates for the Gaussian kernel in the case of densities defined on
, compact domains in and smooth -dimensional sub-manifolds of
the Euclidean space.
We also show experimental results including applications to classification
and semi-supervised learning within the covariate shift framework and
demonstrate some encouraging experimental comparisons. We also show how the
parameters of our algorithms can be chosen in a completely unsupervised manner.Comment: Fixing a few typos in last versio
Combining predictions from linear models when training and test inputs differ
Methods for combining predictions from different models in a supervised
learning setting must somehow estimate/predict the quality of a model's
predictions at unknown future inputs. Many of these methods (often implicitly)
make the assumption that the test inputs are identical to the training inputs,
which is seldom reasonable. By failing to take into account that prediction
will generally be harder for test inputs that did not occur in the training
set, this leads to the selection of too complex models. Based on a novel,
unbiased expression for KL divergence, we propose XAIC and its special case
FAIC as versions of AIC intended for prediction that use different degrees of
knowledge of the test inputs. Both methods substantially differ from and may
outperform all the known versions of AIC even when the training and test inputs
are iid, and are especially useful for deterministic inputs and under covariate
shift. Our experiments on linear models suggest that if the test and training
inputs differ substantially, then XAIC and FAIC predictively outperform AIC,
BIC and several other methods including Bayesian model averaging.Comment: 12 pages, 2 figures. To appear in Proceedings of the 30th Conference
on Uncertainty in Artificial Intelligence (UAI2014). This version includes
the supplementary material (regularity assumptions, proofs
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