1,424 research outputs found
NATURAL ALGORITHMS IN DIGITAL FILTER DESIGN
Digital filters are an important part of Digital Signal Processing (DSP), which plays
vital roles within the modern world, but their design is a complex task requiring a great
deal of specialised knowledge. An analysis of this design process is presented, which
identifies opportunities for the application of optimisation.
The Genetic Algorithm (GA) and Simulated Annealing are problem-independent
and increasingly popular optimisation techniques. They do not require detailed prior
knowledge of the nature of a problem, and are unaffected by a discontinuous search
space, unlike traditional methods such as calculus and hill-climbing.
Potential applications of these techniques to the filter design process are discussed,
and presented with practical results. Investigations into the design of Frequency Sampling
(FS) Finite Impulse Response (FIR) filters using a hybrid GA/hill-climber proved
especially successful, improving on published results. An analysis of the search space
for FS filters provided useful information on the performance of the optimisation technique.
The ability of the GA to trade off a filter's performance with respect to several design
criteria simultaneously, without intervention by the designer, is also investigated.
Methods of simplifying the design process by using this technique are presented, together
with an analysis of the difficulty of the non-linear FIR filter design problem from
a GA perspective. This gave an insight into the fundamental nature of the optimisation
problem, and also suggested future improvements.
The results gained from these investigations allowed the framework for a potential
'intelligent' filter design system to be proposed, in which embedded expert knowledge,
Artificial Intelligence techniques and traditional design methods work together. This
could deliver a single tool capable of designing a wide range of filters with minimal
human intervention, and of proposing solutions to incomplete problems. It could also
provide the basis for the development of tools for other areas of DSP system design
Graph Oracle Models, Lower Bounds, and Gaps for Parallel Stochastic Optimization
We suggest a general oracle-based framework that captures different parallel
stochastic optimization settings described by a dependency graph, and derive
generic lower bounds in terms of this graph. We then use the framework and
derive lower bounds for several specific parallel optimization settings,
including delayed updates and parallel processing with intermittent
communication. We highlight gaps between lower and upper bounds on the oracle
complexity, and cases where the "natural" algorithms are not known to be
optimal
A Measure of Space for Computing over the Reals
We propose a new complexity measure of space for the BSS model of
computation. We define LOGSPACE\_W and PSPACE\_W complexity classes over the
reals. We prove that LOGSPACE\_W is included in NC^2\_R and in P\_W, i.e. is
small enough for being relevant. We prove that the Real Circuit Decision
Problem is P\_R-complete under LOGSPACE\_W reductions, i.e. that LOGSPACE\_W is
large enough for containing natural algorithms. We also prove that PSPACE\_W is
included in PAR\_R
Motif counting beyond five nodes
Counting graphlets is a well-studied problem in graph mining and social network analysis. Recently, several papers explored very simple and natural algorithms based on Monte Carlo sampling of Markov Chains (MC), and reported encouraging results. We show, perhaps surprisingly, that such algorithms are outperformed by color coding (CC) [2], a sophisticated algorithmic technique that we extend to the case of graphlet sampling and for which we prove strong statistical guarantees. Our computational experiments on graphs with millions of nodes show CC to be more accurate than MC; furthermore, we formally show that the mixing time of the MC approach is too high in general, even when the input graph has high conductance. All this comes at a price however. While MC is very efficient in terms of space, CC’s memory requirements become demanding when the size of the input graph and that of the graphlets grow. And yet, our experiments show that CC can push the limits of the state-of-the-art, both in terms of the size of the input graph and of that of the graphlets
The Limits of Post-Selection Generalization
While statistics and machine learning offers numerous methods for ensuring
generalization, these methods often fail in the presence of adaptivity---the
common practice in which the choice of analysis depends on previous
interactions with the same dataset. A recent line of work has introduced
powerful, general purpose algorithms that ensure post hoc generalization (also
called robust or post-selection generalization), which says that, given the
output of the algorithm, it is hard to find any statistic for which the data
differs significantly from the population it came from.
In this work we show several limitations on the power of algorithms
satisfying post hoc generalization. First, we show a tight lower bound on the
error of any algorithm that satisfies post hoc generalization and answers
adaptively chosen statistical queries, showing a strong barrier to progress in
post selection data analysis. Second, we show that post hoc generalization is
not closed under composition, despite many examples of such algorithms
exhibiting strong composition properties
- …