2,622 research outputs found
Storage capacity of a constructive learning algorithm
Upper and lower bounds for the typical storage capacity of a constructive
algorithm, the Tilinglike Learning Algorithm for the Parity Machine [M. Biehl
and M. Opper, Phys. Rev. A {\bf 44} 6888 (1991)], are determined in the
asymptotic limit of large training set sizes. The properties of a perceptron
with threshold, learning a training set of patterns having a biased
distribution of targets, needed as an intermediate step in the capacity
calculation, are determined analytically. The lower bound for the capacity,
determined with a cavity method, is proportional to the number of hidden units.
The upper bound, obtained with the hypothesis of replica symmetry, is close to
the one predicted by Mitchinson and Durbin [Biol. Cyber. {\bf 60} 345 (1989)].Comment: 13 pages, 1 figur
Optimizing 0/1 Loss for Perceptrons by Random Coordinate Descent
The 0/1 loss is an important cost function for perceptrons. Nevertheless it cannot be easily minimized by most existing perceptron learning algorithms. In this paper, we propose a family of random coordinate descent algorithms to directly minimize the 0/1 loss for perceptrons, and prove their convergence. Our algorithms are computationally efficient, and usually achieve the lowest 0/1 loss compared with other algorithms. Such advantages make them favorable for nonseparable real-world problems. Experiments show that our algorithms are especially useful for ensemble learning, and could achieve the lowest test error for many complex data sets when coupled with AdaBoost
Functional Multi-Layer Perceptron: a Nonlinear Tool for Functional Data Analysis
In this paper, we study a natural extension of Multi-Layer Perceptrons (MLP)
to functional inputs. We show that fundamental results for classical MLP can be
extended to functional MLP. We obtain universal approximation results that show
the expressive power of functional MLP is comparable to that of numerical MLP.
We obtain consistency results which imply that the estimation of optimal
parameters for functional MLP is statistically well defined. We finally show on
simulated and real world data that the proposed model performs in a very
satisfactory way.Comment: http://www.sciencedirect.com/science/journal/0893608
Weighted Polynomial Approximations: Limits for Learning and Pseudorandomness
Polynomial approximations to boolean functions have led to many positive
results in computer science. In particular, polynomial approximations to the
sign function underly algorithms for agnostically learning halfspaces, as well
as pseudorandom generators for halfspaces. In this work, we investigate the
limits of these techniques by proving inapproximability results for the sign
function.
Firstly, the polynomial regression algorithm of Kalai et al. (SIAM J. Comput.
2008) shows that halfspaces can be learned with respect to log-concave
distributions on in the challenging agnostic learning model. The
power of this algorithm relies on the fact that under log-concave
distributions, halfspaces can be approximated arbitrarily well by low-degree
polynomials. We ask whether this technique can be extended beyond log-concave
distributions, and establish a negative result. We show that polynomials of any
degree cannot approximate the sign function to within arbitrarily low error for
a large class of non-log-concave distributions on the real line, including
those with densities proportional to .
Secondly, we investigate the derandomization of Chernoff-type concentration
inequalities. Chernoff-type tail bounds on sums of independent random variables
have pervasive applications in theoretical computer science. Schmidt et al.
(SIAM J. Discrete Math. 1995) showed that these inequalities can be established
for sums of random variables with only -wise independence,
for a tail probability of . We show that their results are tight up to
constant factors.
These results rely on techniques from weighted approximation theory, which
studies how well functions on the real line can be approximated by polynomials
under various distributions. We believe that these techniques will have further
applications in other areas of computer science.Comment: 22 page
Computational physics of the mind
In the XIX century and earlier such physicists as Newton, Mayer, Hooke, Helmholtz and Mach were actively engaged in the research on psychophysics, trying to relate psychological sensations to intensities of physical stimuli. Computational physics allows to simulate complex neural processes giving a chance to answer not only the original psychophysical questions but also to create models of mind. In this paper several approaches relevant to modeling of mind are outlined. Since direct modeling of the brain functions is rather limited due to the complexity of such models a number of approximations is introduced. The path from the brain, or computational neurosciences, to the mind, or cognitive sciences, is sketched, with emphasis on higher cognitive functions such as memory and consciousness. No fundamental problems in understanding of the mind seem to arise. From computational point of view realistic models require massively parallel architectures
Advances in quantum machine learning
Here we discuss advances in the field of quantum machine learning. The
following document offers a hybrid discussion; both reviewing the field as it
is currently, and suggesting directions for further research. We include both
algorithms and experimental implementations in the discussion. The field's
outlook is generally positive, showing significant promise. However, we believe
there are appreciable hurdles to overcome before one can claim that it is a
primary application of quantum computation.Comment: 38 pages, 17 Figure
Neurocognitive Informatics Manifesto.
Informatics studies all aspects of the structure of natural and artificial information systems. Theoretical and abstract approaches to information have made great advances, but human information processing is still unmatched in many areas, including information management, representation and understanding. Neurocognitive informatics is a new, emerging field that should help to improve the matching of artificial and natural systems, and inspire better computational algorithms to solve problems that are still beyond the reach of machines. In this position paper examples of neurocognitive inspirations and promising directions in this area are given
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