581 research outputs found
Approximate Message Passing for Underdetermined Audio Source Separation
Approximate message passing (AMP) algorithms have shown great promise in
sparse signal reconstruction due to their low computational requirements and
fast convergence to an exact solution. Moreover, they provide a probabilistic
framework that is often more intuitive than alternatives such as convex
optimisation. In this paper, AMP is used for audio source separation from
underdetermined instantaneous mixtures. In the time-frequency domain, it is
typical to assume a priori that the sources are sparse, so we solve the
corresponding sparse linear inverse problem using AMP. We present a block-based
approach that uses AMP to process multiple time-frequency points
simultaneously. Two algorithms known as AMP and vector AMP (VAMP) are evaluated
in particular. Results show that they are promising in terms of artefact
suppression.Comment: Paper accepted for 3rd International Conference on Intelligent Signal
Processing (ISP 2017
Parameter Estimation in Gaussian Mixture Models with Malicious Noise, without Balanced Mixing Coefficients
We consider the problem of estimating means of two Gaussians in a 2-Gaussian
mixture, which is not balanced and is corrupted by noise of an arbitrary
distribution. We present a robust algorithm to estimate the parameters,
together with upper bounds on the numbers of samples required for the estimate
to be correct, where the bounds are parametrised by the dimension, ratio of the
mixing coefficients, a measure of the separation of the two Gaussians, related
to Mahalanobis distance, and a condition number of the covariance matrix. In
theory, this is the first sample-complexity result for imbalanced mixtures
corrupted by adversarial noise. In practice, our algorithm outperforms the
vanilla Expectation-Maximisation (EM) algorithm in terms of estimation error
Semi-supervised learning of hierarchical latent trait models for data visualisation
An interactive hierarchical Generative Topographic Mapping (HGTM) ¸iteHGTM has been developed to visualise complex data sets. In this paper, we build a more general visualisation system by extending the HGTM visualisation system in 3 directions: bf (1) We generalize HGTM to noise models from the exponential family of distributions. The basic building block is the Latent Trait Model (LTM) developed in ¸iteKabanpami. bf (2) We give the user a choice of initializing the child plots of the current plot in either em interactive, or em automatic mode. In the interactive mode the user interactively selects ``regions of interest'' as in ¸iteHGTM, whereas in the automatic mode an unsupervised minimum message length (MML)-driven construction of a mixture of LTMs is employed. bf (3) We derive general formulas for magnification factors in latent trait models. Magnification factors are a useful tool to improve our understanding of the visualisation plots, since they can highlight the boundaries between data clusters. The unsupervised construction is particularly useful when high-level plots are covered with dense clusters of highly overlapping data projections, making it difficult to use the interactive mode. Such a situation often arises when visualizing large data sets. We illustrate our approach on a toy example and apply our system to three more complex real data sets
Conditional Sampling of Variational Autoencoders via Iterated Approximate Ancestral Sampling
Conditional sampling of variational autoencoders (VAEs) is needed in various applications, such as missing data imputation, but is computationally intractable. A principled choice for asymptotically exact conditional sampling is Metropolis-within-Gibbs (MWG). However, we observe that the tendency of VAEs to learn a structured latent space, a commonly desired property, can cause the MWG sampler to get “stuck” far from the target distribution. This paper mitigates the limitations of MWG: we systematically outline the pitfalls in the context of VAEs, propose two original methods that address these pitfalls, and demonstrate an improved performance of the proposed methods on a set of sampling tasks
Conditional Sampling of Variational Autoencoders via Iterated Approximate Ancestral Sampling
Conditional sampling of variational autoencoders (VAEs) is needed in various
applications, such as missing data imputation, but is computationally
intractable. A principled choice for asymptotically exact conditional sampling
is Metropolis-within-Gibbs (MWG). However, we observe that the tendency of VAEs
to learn a structured latent space, a commonly desired property, can cause the
MWG sampler to get "stuck" far from the target distribution. This paper
mitigates the limitations of MWG: we systematically outline the pitfalls in the
context of VAEs, propose two original methods that address these pitfalls, and
demonstrate an improved performance of the proposed methods on a set of
sampling tasks
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