2,806 research outputs found
Adaptation Algorithm and Theory Based on Generalized Discrepancy
We present a new algorithm for domain adaptation improving upon a discrepancy
minimization algorithm previously shown to outperform a number of algorithms
for this task. Unlike many previous algorithms for domain adaptation, our
algorithm does not consist of a fixed reweighting of the losses over the
training sample. We show that our algorithm benefits from a solid theoretical
foundation and more favorable learning bounds than discrepancy minimization. We
present a detailed description of our algorithm and give several efficient
solutions for solving its optimization problem. We also report the results of
several experiments showing that it outperforms discrepancy minimization
Finding Favourite Tuples on Data Streams with Provably Few Comparisons
One of the most fundamental tasks in data science is to assist a user with
unknown preferences in finding high-utility tuples within a large database. To
accurately elicit the unknown user preferences, a widely-adopted way is by
asking the user to compare pairs of tuples. In this paper, we study the problem
of identifying one or more high-utility tuples by adaptively receiving user
input on a minimum number of pairwise comparisons. We devise a single-pass
streaming algorithm, which processes each tuple in the stream at most once,
while ensuring that the memory size and the number of requested comparisons are
in the worst case logarithmic in , where is the number of all tuples. An
important variant of the problem, which can help to reduce human error in
comparisons, is to allow users to declare ties when confronted with pairs of
tuples of nearly equal utility. We show that the theoretical guarantees of our
method can be maintained for this important problem variant. In addition, we
show how to enhance existing pruning techniques in the literature by leveraging
powerful tools from mathematical programming. Finally, we systematically
evaluate all proposed algorithms over both synthetic and real-life datasets,
examine their scalability, and demonstrate their superior performance over
existing methods.Comment: To appear in KDD 202
Stochastic expansions using continuous dictionaries: L\'{e}vy adaptive regression kernels
This article describes a new class of prior distributions for nonparametric
function estimation. The unknown function is modeled as a limit of weighted
sums of kernels or generator functions indexed by continuous parameters that
control local and global features such as their translation, dilation,
modulation and shape. L\'{e}vy random fields and their stochastic integrals are
employed to induce prior distributions for the unknown functions or,
equivalently, for the number of kernels and for the parameters governing their
features. Scaling, shape, and other features of the generating functions are
location-specific to allow quite different function properties in different
parts of the space, as with wavelet bases and other methods employing
overcomplete dictionaries. We provide conditions under which the stochastic
expansions converge in specified Besov or Sobolev norms. Under a Gaussian error
model, this may be viewed as a sparse regression problem, with regularization
induced via the L\'{e}vy random field prior distribution. Posterior inference
for the unknown functions is based on a reversible jump Markov chain Monte
Carlo algorithm. We compare the L\'{e}vy Adaptive Regression Kernel (LARK)
method to wavelet-based methods using some of the standard test functions, and
illustrate its flexibility and adaptability in nonstationary applications.Comment: Published in at http://dx.doi.org/10.1214/11-AOS889 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Probabilistic Clustering Using Maximal Matrix Norm Couplings
In this paper, we present a local information theoretic approach to
explicitly learn probabilistic clustering of a discrete random variable. Our
formulation yields a convex maximization problem for which it is NP-hard to
find the global optimum. In order to algorithmically solve this optimization
problem, we propose two relaxations that are solved via gradient ascent and
alternating maximization. Experiments on the MSR Sentence Completion Challenge,
MovieLens 100K, and Reuters21578 datasets demonstrate that our approach is
competitive with existing techniques and worthy of further investigation.Comment: Presented at 56th Annual Allerton Conference on Communication,
Control, and Computing, 201
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