t AbstractLeast-squares' sine-fit algorithms are used extensively in signal-processing applications. The parameter estimates produced by such algorithms are subject to both random and systematic errors when the record of input samples consists of a fundamental sine wave corrupted by harmonic distortion or noise. The errors occur because, in general, such sine-fits will incorporate a portion of ...

In this paper, we address a few issues related to the evaluation of the performance of source separation algorithms. We propose several measures of distortion that take into account the gain indeterminacies of BSS algorithms. The total distortion includes interference from the other sources as well as noise and algorithmic artifacts, and we define performance criteria that measure separately th...

Recent results in quantization theory provide theoretical bounds on the distortion of squared-norm based quantizers (see, e.g., [3] or [10]). These bounds are valid whenever the source distribution has a bounded support, regardless of the dimension of the underlying Hilbertian space. However, it remains of interest to select relevant variable for quantization. This task is usually performed usi...

The l2 flattening lemma of Johnson and Lindenstrauss [JL84] is a powerful tool for dimension reduction. It has been conjectured that the target dimension bounds can be refined and bounded in terms of the intrinsic dimensionality of the data set (for example, the doubling dimension). One such problem was proposed by Lang and Plaut [LP01] (see also [GKL03, Mat02, ABN08, CGT10]), and is still open...

Minimum Spanning Trees of weighted graphs are fundamental objects in numerous applications. In particular in distributed networks, the minimum spanning tree of the network is often used to route messages between network nodes. Unfortunately, while being most efficient in the total cost of connecting all nodes, minimum spanning trees fail miserably in the desired property of approximately preser...

We apply the complexity-regularization principle to statistical ill-posed inverse problems in imaging. The class of problems studied includes restoration of images corrupted by Gaussian or Poisson noise and nonlinear transformations. We formulate a natural distortion measure in image space and develop nonasymptotic bounds on estimation performance in terms of an index of resolvability that char...

We show that any q-query locally decodable code (LDC) gives a copy of l 1 with small distortion in the Banach space of q-linear forms on lNp1 ×· · ·× lNpq , provided 1/p1+ · · ·+1/pq ≤ 1 and where k, N , and the distortion are simple functions of the code parameters. We exhibit the copy of l 1 by constructing a basis for it directly from “smooth” LDC decoders. Based on this, we give alternative...

We introduce a randomized iterative fragmentation procedure for finite metric spaces, which is guaranteed to result in a polynomially large subset that is D-equivalent to an ultrametric, where D ∈ (2,∞) is a prescribed target distortion. Since this procedure works for D arbitrarily close to the nonlinear Dvoretzky phase transition at distortion 2, we thus obtain a much simpler probabilistic pro...

This paper studies the fundamental limits of the minimum average length of variable-length compression when a nonzero error probability ǫ is tolerated. We give non-asymptotic bounds on the minimum average length in terms of Erokhin’s rate-distortion function and we use those bounds to obtain a Gaussian approximation on the speed of approach to the limit which is quite accurate for all but small...