The Adaptive Sampling Revisited

The problem of estimating the number $n$ of distinct keys of a large collection of $N$ data is well known in computer science. A classical algorithm is the adaptive sampling (AS). $n$ can be estimated by $R.2^D$, where $R$ is the final bucket (cache) size and $D$ is the final depth at the end of the process. Several new interesting questions can be asked about AS (some of them were suggested by P.Flajolet and popularized by J.Lumbroso). The distribution of $W=\log (R2^D/n)$ is known, we rederive this distribution in a simpler way. We provide new results on the moments of $D$ and $W$. We also analyze the final cache size $R$ distribution. We consider colored keys: assume that among the $n$ distinct keys, $n_C$ do have color $C$. We show how to estimate $p=\frac{n_C}{n}$. We also study colored keys with some multiplicity given by some distribution function. We want to estimate mean an variance of this distribution. Finally, we consider the case where neither colors nor multiplicities are known. There we want to estimate the related parameters. An appendix is devoted to the case where the hashing function provides bits with probability different from $1/2$

Adaptive sampling by information maximization

The investigation of input-output systems often requires a sophisticated choice of test inputs to make best use of limited experimental time. Here we present an iterative algorithm that continuously adjusts an ensemble of test inputs online, subject to the data already acquired about the system under study. The algorithm focuses the input ensemble by maximizing the mutual information between input and output. We apply the algorithm to simulated neurophysiological experiments and show that it serves to extract the ensemble of stimuli that a given neural system ``expects'' as a result of its natural history.Comment: 4 pages, 2 figure

Self-organizing map based adaptive sampling

We propose a new adaptive sampling method that uses Self-Organizing Maps (SOM). In SOM, densely sampled regions in the input space is represented by a larger area on the map than that of sparsely sampled regions. We use this property to progressively tune-in on the interesting region of the design space. The method does not rely on parameterized distribution, and can sample from multi-modal and non-convex distributions. In this paper, we minimize several mathematical test functions. We also show its performance in inequality-constrained objective satisfaction problem, in which the objective is to seek diversity in solutions satisfying certain upper-bound constraint in the minimized objective. A new merit function and a measure of space-filling quality were proposed for this purpose

ADAPTIVE SAMPLING

This paper introduces a new method for signal representation. It is shown that a periodic signal is uniquely defined by its local extrema if the band limit ratio of the signal is less than an octave. A way of adaptive sampling, introduced among these lines, exhibits advantageous properties of possible interest, e.g., for the detection of the pitch frequency