4,387 research outputs found
Hybrid Trilinear and Bilinear Programming for Aligning Partially Overlapping Point Sets
Alignment methods which can handle partially overlapping point sets and are
invariant to the corresponding transformations are desirable in computer
vision, with applications such as providing initial transformation
configuration for local search based methods like ICP. To this end, we first
show that the objective of the robust point matching (RPM) algorithm is a cubic
polynomial. We then utilize the convex envelopes of trilinear and bilinear
monomials to develop its lower bounding function. The resulting lower bounding
problem can be efficiently solved via linear assignment and low dimensional
convex quadratic programming. We next develop a branch-and-bound (BnB)
algorithm which only branches over the transformation parameters and converges
quickly. Experimental results demonstrated favorable performance of the
proposed method over the state-of-the-art methods in terms of robustness and
speed
Planar diagrams from optimization
We propose a new toy model of a heteropolymer chain capable of forming planar
secondary structures typical for RNA molecules. In this model the sequential
intervals between neighboring monomers along a chain are considered as quenched
random variables. Using the optimization procedure for a special class of
concave--type potentials, borrowed from optimal transport analysis, we derive
the local difference equation for the ground state free energy of the chain
with the planar (RNA--like) architecture of paired links. We consider various
distribution functions of intervals between neighboring monomers (truncated
Gaussian and scale--free) and demonstrate the existence of a topological
crossover from sequential to essentially embedded (nested) configurations of
paired links.Comment: 10 pages, 10 figures, the proof is added. arXiv admin note: text
overlap with arXiv:1102.155
Frank-Wolfe Algorithms for Saddle Point Problems
We extend the Frank-Wolfe (FW) optimization algorithm to solve constrained
smooth convex-concave saddle point (SP) problems. Remarkably, the method only
requires access to linear minimization oracles. Leveraging recent advances in
FW optimization, we provide the first proof of convergence of a FW-type saddle
point solver over polytopes, thereby partially answering a 30 year-old
conjecture. We also survey other convergence results and highlight gaps in the
theoretical underpinnings of FW-style algorithms. Motivating applications
without known efficient alternatives are explored through structured prediction
with combinatorial penalties as well as games over matching polytopes involving
an exponential number of constraints.Comment: Appears in: Proceedings of the 20th International Conference on
Artificial Intelligence and Statistics (AISTATS 2017). 39 page
Joint Cuts and Matching of Partitions in One Graph
As two fundamental problems, graph cuts and graph matching have been
investigated over decades, resulting in vast literature in these two topics
respectively. However the way of jointly applying and solving graph cuts and
matching receives few attention. In this paper, we first formalize the problem
of simultaneously cutting a graph into two partitions i.e. graph cuts and
establishing their correspondence i.e. graph matching. Then we develop an
optimization algorithm by updating matching and cutting alternatively, provided
with theoretical analysis. The efficacy of our algorithm is verified on both
synthetic dataset and real-world images containing similar regions or
structures
Fast non-negative deconvolution for spike train inference from population calcium imaging
Calcium imaging for observing spiking activity from large populations of
neurons are quickly gaining popularity. While the raw data are fluorescence
movies, the underlying spike trains are of interest. This work presents a fast
non-negative deconvolution filter to infer the approximately most likely spike
train for each neuron, given the fluorescence observations. This algorithm
outperforms optimal linear deconvolution (Wiener filtering) on both simulated
and biological data. The performance gains come from restricting the inferred
spike trains to be positive (using an interior-point method), unlike the Wiener
filter. The algorithm is fast enough that even when imaging over 100 neurons,
inference can be performed on the set of all observed traces faster than
real-time. Performing optimal spatial filtering on the images further refines
the estimates. Importantly, all the parameters required to perform the
inference can be estimated using only the fluorescence data, obviating the need
to perform joint electrophysiological and imaging calibration experiments.Comment: 22 pages, 10 figure
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