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Chord sequences are a compact and useful description of music, representing each beat or measure in terms of a likely distribution over individual notes without specifying the notes exactly. Transcribing music audio into chord sequences is essential for harmonic analysis, and would be an important component in content-based retrieval and indexing, but… (More)

SUMMARY We examine the effect of clamping variables for approximate inference in undirected graphical models with pairwise relationships and discrete variables. • For any number of variable labels, we demonstrate that clamping and summing approximate sub-partition functions can lead only to a decrease in the partition function estimate for TRW, and an… (More)

For the MIREX 2010 Audio Chord Extraction task, we submitted a total of four systems. Our base system is a trainable chord recognizer based on two-band chroma representations and using a Structured SVM classifier to replace the more familiar hidden Markov model. We submit two versions of this system, one which transposes all training data through all 12… (More)

When belief propagation (BP) converges, it does so to a stationary point of the Bethe free energy F , and is often strikingly accurate. However , it may converge only to a local optimum or may not converge at all. An algorithm was recently introduced by Weller and Jebara for attractive binary pairwise MRFs which is guaranteed to return an-approximation to… (More)

Finding the most likely (MAP) configuration of a Markov random field (MRF) is NP-hard in general. A promising, recent technique is to reduce the problem to finding a maximum weight stable set (MWSS) on a derived weighted graph, which if perfect, allows inference in polynomial time. We derive new results for this approach, including a general decomposition… (More)

—Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference, however, even for this restricted class, is in #P. We prove new formulations of derivatives of the Bethe free energy,… (More)

It was recently proved using graph covers (Ruozzi, 2012) that the Bethe partition function is upper bounded by the true partition function for a binary pairwise model that is attractive. Here we provide a new, arguably simpler proof from first principles. We make use of the idea of clamping a variable to a particular value. For an attractive model, we show… (More)

Belief propagation is a remarkably effective tool for inference, even when applied to networks with cycles. It may be viewed as a way to seek the minimum of the Bethe free energy, though with no convergence guarantee in general. A variational perspective shows that, compared to exact inference, this minimization employs two forms of approximation: (i) the… (More)

- Adrian Weller
- UAI
- 2015

For undirected graphical models, belief propagation often performs remarkably well for approximate marginal inference, and may be viewed as a heuristic to minimize the Bethe free energy. Fo-cusing on binary pairwise models, we demonstrate that several recent results on the Bethe approximation may be generalized to a broad family of related pairwise free… (More)

Linear programming (LP) relaxations are widely used to attempt to identify a most likely configuration of a discrete graphical model. In some cases, the LP relaxation attains an optimum ver-tex at an integral location and thus guarantees an exact solution to the original optimization problem. When this occurs, we say that the LP relaxation is tight. Here we… (More)