1,082 research outputs found
Online Matrix Completion with Side Information
We give an online algorithm and prove novel mistake and regret bounds for
online binary matrix completion with side information. The mistake bounds we
prove are of the form . The term is
analogous to the usual margin term in SVM (perceptron) bounds. More
specifically, if we assume that there is some factorization of the underlying
matrix into where the rows of are interpreted
as "classifiers" in and the rows of as "instances" in
, then is the maximum (normalized) margin over all
factorizations consistent with the observed matrix. The
quasi-dimension term measures the quality of side information. In the
presence of vacuous side information, . However, if the side
information is predictive of the underlying factorization of the matrix, then
in an ideal case, where is the number of distinct row
factors and is the number of distinct column factors. We additionally
provide a generalization of our algorithm to the inductive setting. In this
setting, we provide an example where the side information is not directly
specified in advance. For this example, the quasi-dimension is now bounded
by
Surrogate Functions for Maximizing Precision at the Top
The problem of maximizing precision at the top of a ranked list, often dubbed
Precision@k (prec@k), finds relevance in myriad learning applications such as
ranking, multi-label classification, and learning with severe label imbalance.
However, despite its popularity, there exist significant gaps in our
understanding of this problem and its associated performance measure.
The most notable of these is the lack of a convex upper bounding surrogate
for prec@k. We also lack scalable perceptron and stochastic gradient descent
algorithms for optimizing this performance measure. In this paper we make key
contributions in these directions. At the heart of our results is a family of
truly upper bounding surrogates for prec@k. These surrogates are motivated in a
principled manner and enjoy attractive properties such as consistency to prec@k
under various natural margin/noise conditions.
These surrogates are then used to design a class of novel perceptron
algorithms for optimizing prec@k with provable mistake bounds. We also devise
scalable stochastic gradient descent style methods for this problem with
provable convergence bounds. Our proofs rely on novel uniform convergence
bounds which require an in-depth analysis of the structural properties of
prec@k and its surrogates. We conclude with experimental results comparing our
algorithms with state-of-the-art cutting plane and stochastic gradient
algorithms for maximizing [email protected]: To appear in the the proceedings of the 32nd International Conference
on Machine Learning (ICML 2015
Selective Sampling with Drift
Recently there has been much work on selective sampling, an online active
learning setting, in which algorithms work in rounds. On each round an
algorithm receives an input and makes a prediction. Then, it can decide whether
to query a label, and if so to update its model, otherwise the input is
discarded. Most of this work is focused on the stationary case, where it is
assumed that there is a fixed target model, and the performance of the
algorithm is compared to a fixed model. However, in many real-world
applications, such as spam prediction, the best target function may drift over
time, or have shifts from time to time. We develop a novel selective sampling
algorithm for the drifting setting, analyze it under no assumptions on the
mechanism generating the sequence of instances, and derive new mistake bounds
that depend on the amount of drift in the problem. Simulations on synthetic and
real-world datasets demonstrate the superiority of our algorithms as a
selective sampling algorithm in the drifting setting
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