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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)

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)

- Allen C Templeton, Shaowei Chen, Stephen M Gross, Royce W Murray, T Vossmeyer, L Katsikas +68 others
- 1998

Isolable, water-soluble gold clusters protected by monolayers of tiopronin (tiopronin-MPCs) or coenzyme A (CoA-MPCs) were synthesized by a procedure of comparable simplicity to the Brust synthesis for alkanethiolate monolayer-protected gold clusters. High-resolution transmission electron microscopy shows that, like their alkanethiolate-MPC counterparts, the… (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)