5,073 research outputs found
Distribution-Independent Evolvability of Linear Threshold Functions
Valiant's (2007) model of evolvability models the evolutionary process of
acquiring useful functionality as a restricted form of learning from random
examples. Linear threshold functions and their various subclasses, such as
conjunctions and decision lists, play a fundamental role in learning theory and
hence their evolvability has been the primary focus of research on Valiant's
framework (2007). One of the main open problems regarding the model is whether
conjunctions are evolvable distribution-independently (Feldman and Valiant,
2008). We show that the answer is negative. Our proof is based on a new
combinatorial parameter of a concept class that lower-bounds the complexity of
learning from correlations.
We contrast the lower bound with a proof that linear threshold functions
having a non-negligible margin on the data points are evolvable
distribution-independently via a simple mutation algorithm. Our algorithm
relies on a non-linear loss function being used to select the hypotheses
instead of 0-1 loss in Valiant's (2007) original definition. The proof of
evolvability requires that the loss function satisfies several mild conditions
that are, for example, satisfied by the quadratic loss function studied in
several other works (Michael, 2007; Feldman, 2009; Valiant, 2010). An important
property of our evolution algorithm is monotonicity, that is the algorithm
guarantees evolvability without any decreases in performance. Previously,
monotone evolvability was only shown for conjunctions with quadratic loss
(Feldman, 2009) or when the distribution on the domain is severely restricted
(Michael, 2007; Feldman, 2009; Kanade et al., 2010
A Complete Characterization of Statistical Query Learning with Applications to Evolvability
Statistical query (SQ) learning model of Kearns (1993) is a natural
restriction of the PAC learning model in which a learning algorithm is allowed
to obtain estimates of statistical properties of the examples but cannot see
the examples themselves. We describe a new and simple characterization of the
query complexity of learning in the SQ learning model. Unlike the previously
known bounds on SQ learning our characterization preserves the accuracy and the
efficiency of learning. The preservation of accuracy implies that that our
characterization gives the first characterization of SQ learning in the
agnostic learning framework. The preservation of efficiency is achieved using a
new boosting technique and allows us to derive a new approach to the design of
evolutionary algorithms in Valiant's (2006) model of evolvability. We use this
approach to demonstrate the existence of a large class of monotone evolutionary
learning algorithms based on square loss performance estimation. These results
differ significantly from the few known evolutionary algorithms and give
evidence that evolvability in Valiant's model is a more versatile phenomenon
than there had been previous reason to suspect.Comment: Simplified Lemma 3.8 and it's application
Scaling properties of protein family phylogenies
One of the classical questions in evolutionary biology is how evolutionary
processes are coupled at the gene and species level. With this motivation, we
compare the topological properties (mainly the depth scaling, as a
characterization of balance) of a large set of protein phylogenies with a set
of species phylogenies. The comparative analysis shows that both sets of
phylogenies share remarkably similar scaling behavior, suggesting the
universality of branching rules and of the evolutionary processes that drive
biological diversification from gene to species level. In order to explain such
generality, we propose a simple model which allows us to estimate the
proportion of evolvability/robustness needed to approximate the scaling
behavior observed in the phylogenies, highlighting the relevance of the
robustness of a biological system (species or protein) in the scaling
properties of the phylogenetic trees. Thus, the rules that govern the
incapability of a biological system to diversify are equally relevant both at
the gene and at the species level.Comment: Replaced with final published versio
Measuring the Evolvability Landscape to study Neutrality
This theoretical work defines the measure of autocorrelation of evolvability
in the context of neutral fitness landscape. This measure has been studied on
the classical MAX-SAT problem. This work highlight a new characteristic of
neutral fitness landscapes which allows to design new adapted metaheuristic
Evolution with Drifting Targets
We consider the question of the stability of evolutionary algorithms to
gradual changes, or drift, in the target concept. We define an algorithm to be
resistant to drift if, for some inverse polynomial drift rate in the target
function, it converges to accuracy 1 -- \epsilon , with polynomial resources,
and then stays within that accuracy indefinitely, except with probability
\epsilon , at any one time. We show that every evolution algorithm, in the
sense of Valiant (2007; 2009), can be converted using the Correlational Query
technique of Feldman (2008), into such a drift resistant algorithm. For certain
evolutionary algorithms, such as for Boolean conjunctions, we give bounds on
the rates of drift that they can resist. We develop some new evolution
algorithms that are resistant to significant drift. In particular, we give an
algorithm for evolving linear separators over the spherically symmetric
distribution that is resistant to a drift rate of O(\epsilon /n), and another
algorithm over the more general product normal distributions that resists a
smaller drift rate.
The above translation result can be also interpreted as one on the robustness
of the notion of evolvability itself under changes of definition. As a second
result in that direction we show that every evolution algorithm can be
converted to a quasi-monotonic one that can evolve from any starting point
without the performance ever dipping significantly below that of the starting
point. This permits the somewhat unnatural feature of arbitrary performance
degradations to be removed from several known robustness translations
Scaling laws in bacterial genomes: A side-effect of selection of mutational robustness?
In the past few years, numerous research projects have focused on identifying and understanding scaling properties in the gene content of prokaryote genomes and the intricacy of their regulation networks. Yet, and despite the increasing amount of data available, the origins of these scalings remain an open question. The RAevol model, a digital genetics model, provides us with an insight into the mechanisms involved in an evolutionary process. The results we present here show that (i) our model reproduces qualitatively these scaling laws and that (ii) these laws are not due to differences in lifestyles but to differences in the spontaneous rates of mutations and rearrangements. We argue that this is due to an indirect selective pressure for robustness that constrains the genome size
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