22,612 research outputs found
Perfect Computational Equivalence between Quantum Turing Machines and Finitely Generated Uniform Quantum Circuit Families
In order to establish the computational equivalence between quantum Turing
machines (QTMs) and quantum circuit families (QCFs) using Yao's quantum circuit
simulation of QTMs, we previously introduced the class of uniform QCFs based on
an infinite set of elementary gates, which has been shown to be computationally
equivalent to the polynomial-time QTMs (with appropriate restriction of
amplitudes) up to bounded error simulation. This result implies that the
complexity class BQP introduced by Bernstein and Vazirani for QTMs equals its
counterpart for uniform QCFs. However, the complexity classes ZQP and EQP for
QTMs do not appear to equal their counterparts for uniform QCFs. In this paper,
we introduce a subclass of uniform QCFs, the finitely generated uniform QCFs,
based on finite number of elementary gates and show that the class of finitely
generated uniform QCFs is perfectly equivalent to the class of polynomial-time
QTMs; they can exactly simulate each other. This naturally implies that BQP as
well as ZQP and EQP equal the corresponding complexity classes of the finitely
generated uniform QCFs.Comment: 11page
Exponential Machines
Modeling interactions between features improves the performance of machine
learning solutions in many domains (e.g. recommender systems or sentiment
analysis). In this paper, we introduce Exponential Machines (ExM), a predictor
that models all interactions of every order. The key idea is to represent an
exponentially large tensor of parameters in a factorized format called Tensor
Train (TT). The Tensor Train format regularizes the model and lets you control
the number of underlying parameters. To train the model, we develop a
stochastic Riemannian optimization procedure, which allows us to fit tensors
with 2^160 entries. We show that the model achieves state-of-the-art
performance on synthetic data with high-order interactions and that it works on
par with high-order factorization machines on a recommender system dataset
MovieLens 100K.Comment: ICLR-2017 workshop track pape
Quantum machine learning: a classical perspective
Recently, increased computational power and data availability, as well as
algorithmic advances, have led machine learning techniques to impressive
results in regression, classification, data-generation and reinforcement
learning tasks. Despite these successes, the proximity to the physical limits
of chip fabrication alongside the increasing size of datasets are motivating a
growing number of researchers to explore the possibility of harnessing the
power of quantum computation to speed-up classical machine learning algorithms.
Here we review the literature in quantum machine learning and discuss
perspectives for a mixed readership of classical machine learning and quantum
computation experts. Particular emphasis will be placed on clarifying the
limitations of quantum algorithms, how they compare with their best classical
counterparts and why quantum resources are expected to provide advantages for
learning problems. Learning in the presence of noise and certain
computationally hard problems in machine learning are identified as promising
directions for the field. Practical questions, like how to upload classical
data into quantum form, will also be addressed.Comment: v3 33 pages; typos corrected and references adde
Sharp analysis of low-rank kernel matrix approximations
We consider supervised learning problems within the positive-definite kernel
framework, such as kernel ridge regression, kernel logistic regression or the
support vector machine. With kernels leading to infinite-dimensional feature
spaces, a common practical limiting difficulty is the necessity of computing
the kernel matrix, which most frequently leads to algorithms with running time
at least quadratic in the number of observations n, i.e., O(n^2). Low-rank
approximations of the kernel matrix are often considered as they allow the
reduction of running time complexities to O(p^2 n), where p is the rank of the
approximation. The practicality of such methods thus depends on the required
rank p. In this paper, we show that in the context of kernel ridge regression,
for approximations based on a random subset of columns of the original kernel
matrix, the rank p may be chosen to be linear in the degrees of freedom
associated with the problem, a quantity which is classically used in the
statistical analysis of such methods, and is often seen as the implicit number
of parameters of non-parametric estimators. This result enables simple
algorithms that have sub-quadratic running time complexity, but provably
exhibit the same predictive performance than existing algorithms, for any given
problem instance, and not only for worst-case situations
An ontology enhanced parallel SVM for scalable spam filter training
This is the post-print version of the final paper published in Neurocomputing. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2013 Elsevier B.V.Spam, under a variety of shapes and forms, continues to inflict increased damage. Varying approaches including Support Vector Machine (SVM) techniques have been proposed for spam filter training and classification. However, SVM training is a computationally intensive process. This paper presents a MapReduce based parallel SVM algorithm for scalable spam filter training. By distributing, processing and optimizing the subsets of the training data across multiple participating computer nodes, the parallel SVM reduces the training time significantly. Ontology semantics are employed to minimize the impact of accuracy degradation when distributing the training data among a number of SVM classifiers. Experimental results show that ontology based augmentation improves the accuracy level of the parallel SVM beyond the original sequential counterpart
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