8,105 research outputs found
Local Algorithms for Block Models with Side Information
There has been a recent interest in understanding the power of local
algorithms for optimization and inference problems on sparse graphs. Gamarnik
and Sudan (2014) showed that local algorithms are weaker than global algorithms
for finding large independent sets in sparse random regular graphs. Montanari
(2015) showed that local algorithms are suboptimal for finding a community with
high connectivity in the sparse Erd\H{o}s-R\'enyi random graphs. For the
symmetric planted partition problem (also named community detection for the
block models) on sparse graphs, a simple observation is that local algorithms
cannot have non-trivial performance.
In this work we consider the effect of side information on local algorithms
for community detection under the binary symmetric stochastic block model. In
the block model with side information each of the vertices is labeled
or independently and uniformly at random; each pair of vertices is
connected independently with probability if both of them have the same
label or otherwise. The goal is to estimate the underlying vertex
labeling given 1) the graph structure and 2) side information in the form of a
vertex labeling positively correlated with the true one. Assuming that the
ratio between in and out degree is and the average degree , we characterize three different regimes under which a
local algorithm, namely, belief propagation run on the local neighborhoods,
maximizes the expected fraction of vertices labeled correctly. Thus, in
contrast to the case of symmetric block models without side information, we
show that local algorithms can achieve optimal performance for the block model
with side information.Comment: Due to the limitation "The abstract field cannot be longer than 1,920
characters", the abstract here is shorter than that in the PDF fil
Weighted ℓ_1 minimization for sparse recovery with prior information
In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In particular, we focus on a model where the entries of the unknown vector fall into two sets, each with a different probability of being nonzero. We propose a weighted ℓ_1 minimization recovery algorithm and analyze its performance using a Grassman angle approach. We compute explicitly the relationship between the system parameters (the weights, the number of measurements, the size of the two sets, the probabilities of being non-zero) so that an iid random Gaussian measurement matrix along with weighted ℓ_1 minimization recovers almost all such sparse signals with overwhelming probability as the problem dimension increases. This allows us to compute the optimal weights. We also provide simulations to demonstrate the advantages of the method over conventional ℓ_1 optimization
MRFalign: Protein Homology Detection through Alignment of Markov Random Fields
Sequence-based protein homology detection has been extensively studied and so
far the most sensitive method is based upon comparison of protein sequence
profiles, which are derived from multiple sequence alignment (MSA) of sequence
homologs in a protein family. A sequence profile is usually represented as a
position-specific scoring matrix (PSSM) or an HMM (Hidden Markov Model) and
accordingly PSSM-PSSM or HMM-HMM comparison is used for homolog detection. This
paper presents a new homology detection method MRFalign, consisting of three
key components: 1) a Markov Random Fields (MRF) representation of a protein
family; 2) a scoring function measuring similarity of two MRFs; and 3) an
efficient ADMM (Alternating Direction Method of Multipliers) algorithm aligning
two MRFs. Compared to HMM that can only model very short-range residue
correlation, MRFs can model long-range residue interaction pattern and thus,
encode information for the global 3D structure of a protein family.
Consequently, MRF-MRF comparison for remote homology detection shall be much
more sensitive than HMM-HMM or PSSM-PSSM comparison. Experiments confirm that
MRFalign outperforms several popular HMM or PSSM-based methods in terms of both
alignment accuracy and remote homology detection and that MRFalign works
particularly well for mainly beta proteins. For example, tested on the
benchmark SCOP40 (8353 proteins) for homology detection, PSSM-PSSM and HMM-HMM
succeed on 48% and 52% of proteins, respectively, at superfamily level, and on
15% and 27% of proteins, respectively, at fold level. In contrast, MRFalign
succeeds on 57.3% and 42.5% of proteins at superfamily and fold level,
respectively. This study implies that long-range residue interaction patterns
are very helpful for sequence-based homology detection. The software is
available for download at http://raptorx.uchicago.edu/download/.Comment: Accepted by both RECOMB 2014 and PLOS Computational Biolog
Asymmetric Pruning for Learning Cascade Detectors
Cascade classifiers are one of the most important contributions to real-time
object detection. Nonetheless, there are many challenging problems arising in
training cascade detectors. One common issue is that the node classifier is
trained with a symmetric classifier. Having a low misclassification error rate
does not guarantee an optimal node learning goal in cascade classifiers, i.e.,
an extremely high detection rate with a moderate false positive rate. In this
work, we present a new approach to train an effective node classifier in a
cascade detector. The algorithm is based on two key observations: 1) Redundant
weak classifiers can be safely discarded; 2) The final detector should satisfy
the asymmetric learning objective of the cascade architecture. To achieve this,
we separate the classifier training into two steps: finding a pool of
discriminative weak classifiers/features and training the final classifier by
pruning weak classifiers which contribute little to the asymmetric learning
criterion (asymmetric classifier construction). Our model reduction approach
helps accelerate the learning time while achieving the pre-determined learning
objective. Experimental results on both face and car data sets verify the
effectiveness of the proposed algorithm. On the FDDB face data sets, our
approach achieves the state-of-the-art performance, which demonstrates the
advantage of our approach.Comment: 14 page
Mental state estimation for brain-computer interfaces
Mental state estimation is potentially useful for the development of asynchronous brain-computer interfaces. In this study, four mental states have been identified and decoded from the electrocorticograms (ECoGs) of six epileptic patients, engaged in a memory reach task. A novel signal analysis technique has been applied to high-dimensional, statistically sparse ECoGs recorded by a large number of electrodes. The strength of the proposed technique lies in its ability to jointly extract spatial and temporal patterns, responsible for encoding mental state differences. As such, the technique offers a systematic way of analyzing the spatiotemporal aspects of brain information processing and may be applicable to a wide range of spatiotemporal neurophysiological signals
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