3,400 research outputs found
Visualising Basins of Attraction for the Cross-Entropy and the Squared Error Neural Network Loss Functions
Quantification of the stationary points and the associated basins of
attraction of neural network loss surfaces is an important step towards a
better understanding of neural network loss surfaces at large. This work
proposes a novel method to visualise basins of attraction together with the
associated stationary points via gradient-based random sampling. The proposed
technique is used to perform an empirical study of the loss surfaces generated
by two different error metrics: quadratic loss and entropic loss. The empirical
observations confirm the theoretical hypothesis regarding the nature of neural
network attraction basins. Entropic loss is shown to exhibit stronger gradients
and fewer stationary points than quadratic loss, indicating that entropic loss
has a more searchable landscape. Quadratic loss is shown to be more resilient
to overfitting than entropic loss. Both losses are shown to exhibit local
minima, but the number of local minima is shown to decrease with an increase in
dimensionality. Thus, the proposed visualisation technique successfully
captures the local minima properties exhibited by the neural network loss
surfaces, and can be used for the purpose of fitness landscape analysis of
neural networks.Comment: Preprint submitted to the Neural Networks journa
Frequency Effects on Predictability of Stock Returns
We propose that predictability is a prerequisite for profitability on
financial markets. We look at ways to measure predictability of price changes
using information theoretic approach and employ them on all historical data
available for NYSE 100 stocks. This allows us to determine whether frequency of
sampling price changes affects the predictability of those. We also relations
between price changes predictability and the deviation of the price formation
processes from iid as well as the stock's sector. We also briefly comment on
the complicated relationship between predictability of price changes and the
profitability of algorithmic trading.Comment: 8 pages, 16 figures, submitted for possible publication to
Computational Intelligence for Financial Engineering and Economics 2014
conferenc
First-principles calculation of DNA looping in tethered particle experiments
We calculate the probability of DNA loop formation mediated by regulatory
proteins such as Lac repressor (LacI), using a mathematical model of DNA
elasticity. Our model is adapted to calculating quantities directly observable
in Tethered Particle Motion (TPM) experiments, and it accounts for all the
entropic forces present in such experiments. Our model has no free parameters;
it characterizes DNA elasticity using information obtained in other kinds of
experiments. [...] We show how to compute both the "looping J factor" (or
equivalently, the looping free energy) for various DNA construct geometries and
LacI concentrations, as well as the detailed probability density function of
bead excursions. We also show how to extract the same quantities from recent
experimental data on tethered particle motion, and then compare to our model's
predictions. [...] Our model successfully reproduces the detailed distributions
of bead excursion, including their surprising three-peak structure, without any
fit parameters and without invoking any alternative conformation of the LacI
tetramer. Indeed, the model qualitatively reproduces the observed dependence of
these distributions on tether length (e.g., phasing) and on LacI concentration
(titration). However, for short DNA loops (around 95 basepairs) the experiments
show more looping than is predicted by the harmonic-elasticity model, echoing
other recent experimental results. Because the experiments we study are done in
vitro, this anomalously high looping cannot be rationalized as resulting from
the presence of DNA-bending proteins or other cellular machinery. We also show
that it is unlikely to be the result of a hypothetical "open" conformation of
the LacI tetramer.Comment: See the supplement at
http://www.physics.upenn.edu/~pcn/Ms/TowlesEtalSuppl.pdf . This revised
version accepted for publication at Physical Biolog
Dynamics of the Wang-Landau algorithm and complexity of rare events for the three-dimensional bimodal Ising spin glass
We investigate the performance of flat-histogram methods based on a
multicanonical ensemble and the Wang-Landau algorithm for the three-dimensional
+/- J spin glass by measuring round-trip times in the energy range between the
zero-temperature ground state and the state of highest energy. Strong
sample-to-sample variations are found for fixed system size and the
distribution of round-trip times follows a fat-tailed Frechet extremal value
distribution. Rare events in the fat tails of these distributions corresponding
to extremely slowly equilibrating spin glass realizations dominate the
calculations of statistical averages. While the typical round-trip time scales
exponential as expected for this NP-hard problem, we find that the average
round-trip time is no longer well-defined for systems with N >= 8^3 spins. We
relate the round-trip times for multicanonical sampling to intrinsic properties
of the energy landscape and compare with the numerical effort needed by the
genetic Cluster-Exact Approximation to calculate the exact ground state
energies. For systems with N >= 8^3 spins the simulation of these rare events
becomes increasingly hard. For N >= 14^3 there are samples where the
Wang-Landau algorithm fails to find the true ground state within reasonable
simulation times. We expect similar behavior for other algorithms based on
multicanonical sampling.Comment: 9 pages, 12 figure
A review of Monte Carlo simulations of polymers with PERM
In this review, we describe applications of the pruned-enriched Rosenbluth
method (PERM), a sequential Monte Carlo algorithm with resampling, to various
problems in polymer physics. PERM produces samples according to any given
prescribed weight distribution, by growing configurations step by step with
controlled bias, and correcting "bad" configurations by "population control".
The latter is implemented, in contrast to other population based algorithms
like e.g. genetic algorithms, by depth-first recursion which avoids storing all
members of the population at the same time in computer memory. The problems we
discuss all concern single polymers (with one exception), but under various
conditions: Homopolymers in good solvents and at the point, semi-stiff
polymers, polymers in confining geometries, stretched polymers undergoing a
forced globule-linear transition, star polymers, bottle brushes, lattice
animals as a model for randomly branched polymers, DNA melting, and finally --
as the only system at low temperatures, lattice heteropolymers as simple models
for protein folding. PERM is for some of these problems the method of choice,
but it can also fail. We discuss how to recognize when a result is reliable,
and we discuss also some types of bias that can be crucial in guiding the
growth into the right directions.Comment: 29 pages, 26 figures, to be published in J. Stat. Phys. (2011
Designing labeled graph classifiers by exploiting the R\'enyi entropy of the dissimilarity representation
Representing patterns as labeled graphs is becoming increasingly common in
the broad field of computational intelligence. Accordingly, a wide repertoire
of pattern recognition tools, such as classifiers and knowledge discovery
procedures, are nowadays available and tested for various datasets of labeled
graphs. However, the design of effective learning procedures operating in the
space of labeled graphs is still a challenging problem, especially from the
computational complexity viewpoint. In this paper, we present a major
improvement of a general-purpose classifier for graphs, which is conceived on
an interplay between dissimilarity representation, clustering,
information-theoretic techniques, and evolutionary optimization algorithms. The
improvement focuses on a specific key subroutine devised to compress the input
data. We prove different theorems which are fundamental to the setting of the
parameters controlling such a compression operation. We demonstrate the
effectiveness of the resulting classifier by benchmarking the developed
variants on well-known datasets of labeled graphs, considering as distinct
performance indicators the classification accuracy, computing time, and
parsimony in terms of structural complexity of the synthesized classification
models. The results show state-of-the-art standards in terms of test set
accuracy and a considerable speed-up for what concerns the computing time.Comment: Revised versio
Semi-automatic selection of summary statistics for ABC model choice
A central statistical goal is to choose between alternative explanatory
models of data. In many modern applications, such as population genetics, it is
not possible to apply standard methods based on evaluating the likelihood
functions of the models, as these are numerically intractable. Approximate
Bayesian computation (ABC) is a commonly used alternative for such situations.
ABC simulates data x for many parameter values under each model, which is
compared to the observed data xobs. More weight is placed on models under which
S(x) is close to S(xobs), where S maps data to a vector of summary statistics.
Previous work has shown the choice of S is crucial to the efficiency and
accuracy of ABC. This paper provides a method to select good summary statistics
for model choice. It uses a preliminary step, simulating many x values from all
models and fitting regressions to this with the model as response. The
resulting model weight estimators are used as S in an ABC analysis. Theoretical
results are given to justify this as approximating low dimensional sufficient
statistics. A substantive application is presented: choosing between competing
coalescent models of demographic growth for Campylobacter jejuni in New Zealand
using multi-locus sequence typing data
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