23,385 research outputs found
Distributed Information Retrieval using Keyword Auctions
This report motivates the need for large-scale distributed approaches to information retrieval, and proposes solutions based on keyword auctions
Matrix Completion from Fewer Entries: Spectral Detectability and Rank Estimation
The completion of low rank matrices from few entries is a task with many
practical applications. We consider here two aspects of this problem:
detectability, i.e. the ability to estimate the rank reliably from the
fewest possible random entries, and performance in achieving small
reconstruction error. We propose a spectral algorithm for these two tasks
called MaCBetH (for Matrix Completion with the Bethe Hessian). The rank is
estimated as the number of negative eigenvalues of the Bethe Hessian matrix,
and the corresponding eigenvectors are used as initial condition for the
minimization of the discrepancy between the estimated matrix and the revealed
entries. We analyze the performance in a random matrix setting using results
from the statistical mechanics of the Hopfield neural network, and show in
particular that MaCBetH efficiently detects the rank of a large
matrix from entries, where is a constant close to .
We also evaluate the corresponding root-mean-square error empirically and show
that MaCBetH compares favorably to other existing approaches.Comment: NIPS Conference 201
Dreaming neural networks: forgetting spurious memories and reinforcing pure ones
The standard Hopfield model for associative neural networks accounts for
biological Hebbian learning and acts as the harmonic oscillator for pattern
recognition, however its maximal storage capacity is , far
from the theoretical bound for symmetric networks, i.e. . Inspired
by sleeping and dreaming mechanisms in mammal brains, we propose an extension
of this model displaying the standard on-line (awake) learning mechanism (that
allows the storage of external information in terms of patterns) and an
off-line (sleep) unlearningconsolidating mechanism (that allows
spurious-pattern removal and pure-pattern reinforcement): this obtained daily
prescription is able to saturate the theoretical bound , remaining
also extremely robust against thermal noise. Both neural and synaptic features
are analyzed both analytically and numerically. In particular, beyond obtaining
a phase diagram for neural dynamics, we focus on synaptic plasticity and we
give explicit prescriptions on the temporal evolution of the synaptic matrix.
We analytically prove that our algorithm makes the Hebbian kernel converge with
high probability to the projection matrix built over the pure stored patterns.
Furthermore, we obtain a sharp and explicit estimate for the "sleep rate" in
order to ensure such a convergence. Finally, we run extensive numerical
simulations (mainly Monte Carlo sampling) to check the approximations
underlying the analytical investigations (e.g., we developed the whole theory
at the so called replica-symmetric level, as standard in the
Amit-Gutfreund-Sompolinsky reference framework) and possible finite-size
effects, finding overall full agreement with the theory.Comment: 31 pages, 12 figure
Convex Optimization Approaches for Blind Sensor Calibration using Sparsity
We investigate a compressive sensing framework in which the sensors introduce
a distortion to the measurements in the form of unknown gains. We focus on
blind calibration, using measures performed on multiple unknown (but sparse)
signals and formulate the joint recovery of the gains and the sparse signals as
a convex optimization problem. We divide this problem in 3 subproblems with
different conditions on the gains, specifially (i) gains with different
amplitude and the same phase, (ii) gains with the same amplitude and different
phase and (iii) gains with different amplitude and phase. In order to solve the
first case, we propose an extension to the basis pursuit optimization which can
estimate the unknown gains along with the unknown sparse signals. For the
second case, we formulate a quadratic approach that eliminates the unknown
phase shifts and retrieves the unknown sparse signals. An alternative form of
this approach is also formulated to reduce complexity and memory requirements
and provide scalability with respect to the number of input signals. Finally
for the third case, we propose a formulation that combines the earlier two
approaches to solve the problem. The performance of the proposed algorithms is
investigated extensively through numerical simulations, which demonstrates that
simultaneous signal recovery and calibration is possible with convex methods
when sufficiently many (unknown, but sparse) calibrating signals are provided
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