2,522 research outputs found
On the Asymptotic Efficiency of Approximate Bayesian Computation Estimators
Many statistical applications involve models for which it is difficult to
evaluate the likelihood, but from which it is relatively easy to sample.
Approximate Bayesian computation is a likelihood-free method for implementing
Bayesian inference in such cases. We present results on the asymptotic variance
of estimators obtained using approximate Bayesian computation in a large-data
limit. Our key assumption is that the data are summarized by a
fixed-dimensional summary statistic that obeys a central limit theorem. We
prove asymptotic normality of the mean of the approximate Bayesian computation
posterior. This result also shows that, in terms of asymptotic variance, we
should use a summary statistic that is the same dimension as the parameter
vector, p; and that any summary statistic of higher dimension can be reduced,
through a linear transformation, to dimension p in a way that can only reduce
the asymptotic variance of the posterior mean. We look at how the Monte Carlo
error of an importance sampling algorithm that samples from the approximate
Bayesian computation posterior affects the accuracy of estimators. We give
conditions on the importance sampling proposal distribution such that the
variance of the estimator will be the same order as that of the maximum
likelihood estimator based on the summary statistics used. This suggests an
iterative importance sampling algorithm, which we evaluate empirically on a
stochastic volatility model.Comment: Main text shortened and proof revised. To appear in Biometrik
An effective likelihood-free approximate computing method with statistical inferential guarantees
Approximate Bayesian computing is a powerful likelihood-free method that has
grown increasingly popular since early applications in population genetics.
However, complications arise in the theoretical justification for Bayesian
inference conducted from this method with a non-sufficient summary statistic.
In this paper, we seek to re-frame approximate Bayesian computing within a
frequentist context and justify its performance by standards set on the
frequency coverage rate. In doing so, we develop a new computational technique
called approximate confidence distribution computing, yielding theoretical
support for the use of non-sufficient summary statistics in likelihood-free
methods. Furthermore, we demonstrate that approximate confidence distribution
computing extends the scope of approximate Bayesian computing to include
data-dependent priors without damaging the inferential integrity. This
data-dependent prior can be viewed as an initial `distribution estimate' of the
target parameter which is updated with the results of the approximate
confidence distribution computing method. A general strategy for constructing
an appropriate data-dependent prior is also discussed and is shown to often
increase the computing speed while maintaining statistical inferential
guarantees. We supplement the theory with simulation studies illustrating the
benefits of the proposed method, namely the potential for broader applications
and the increased computing speed compared to the standard approximate Bayesian
computing methods
Transcription Coupled DNA Repair in Saccharomyces Cerevisiae: the Interplay of Facilitators and Repressors
Nucleotide excision repair (NER) is a multi-step cellular process that removes bulky and/or helix-distorting DNA lesions, such as UV induced cyclobutane pyrimidine dimers (CPDs) and bulky chemical adducts. Transcription coupled repair (TCR) is a subpathway of NER dedicated to rapid removal of lesions in the transcribed strand of actively transcribed genes. The TCR mechanism in bacteria has been relatively well elucidated. However, TCR in eukaryotic cells appears to be extremely complicated. The exact nature of the TCR signal and the mechanism of the transcription-repair coupling have been long-standing enigmas. This dissertation focused on how the TCR repressors and facilitators interplay with RNA polymerase II (RNAP II) to carry out TCR in yeast Saccharomyces cerevisiae. By site-specific incorporation of the unnatural amino acid p-benzoyl-L-phenylalanine, we mapped interactions between Spt5 and RNAP II in S. cerevisiae. Through its KOW4-5 domains, Spt5 extensively interacts with Rpb4/7. Spt5 also interacts with Rpb1 and Rpb2, two largest subunits of RNAP II, at the clamp, protrusion and wall domains. Deletion of Spt5 KOW4-5 domains decreases transcription elongation and derepresses TCR. Our findings suggest that Spt5 is a key coordinator for holding the RNAP II complex in a closed conformation that is highly competent for transcription elongation but repressive to TCR. We also demonstrated that E1103G mutation of Rpb1, the largest subunit of RNAP II, which promotes transcription bypass of UV-induced CPDs, increases survival of UV irradiated yeast cells but attenuates TCR. In contrast, G730D mutation of Rpb1, which abolishes transcription bypass of CPDs, enhances TCR. Our findings suggest that transcription bypass of lesions attenuates TCR but enhances cell tolerance to DNA lesions. Efficient stalling of RNAP II is essential for efficient TCR. Sen1 is an RNA/DNA helicase that has been shown to mediate termination of noncoding RNAs and some mRNAs. Like deletion of Rad26 or Rpb9, the Sen1 N-terminal deletion (1-975 residues) increases the UV sensitivity of the GGR-deficient cells. Moreover, the Sen1 N-terminal deletion decreases TCR in rad7Δ and rad7Δ rad26Δ cells but not that in rad7Δ rpb9Δ cells. Our findings suggest that the N-terminal domain of Sen1 contributes to Rad26-independent TCR
Rewriting Flash Memories by Message Passing
This paper constructs WOM codes that combine rewriting and error correction
for mitigating the reliability and the endurance problems in flash memory. We
consider a rewriting model that is of practical interest to flash applications
where only the second write uses WOM codes. Our WOM code construction is based
on binary erasure quantization with LDGM codes, where the rewriting uses
message passing and has potential to share the efficient hardware
implementations with LDPC codes in practice. We show that the coding scheme
achieves the capacity of the rewriting model. Extensive simulations show that
the rewriting performance of our scheme compares favorably with that of polar
WOM code in the rate region where high rewriting success probability is
desired. We further augment our coding schemes with error correction
capability. By drawing a connection to the conjugate code pairs studied in the
context of quantum error correction, we develop a general framework for
constructing error-correction WOM codes. Under this framework, we give an
explicit construction of WOM codes whose codewords are contained in BCH codes.Comment: Submitted to ISIT 201
Co-occurrence Feature Learning for Skeleton based Action Recognition using Regularized Deep LSTM Networks
Skeleton based action recognition distinguishes human actions using the
trajectories of skeleton joints, which provide a very good representation for
describing actions. Considering that recurrent neural networks (RNNs) with Long
Short-Term Memory (LSTM) can learn feature representations and model long-term
temporal dependencies automatically, we propose an end-to-end fully connected
deep LSTM network for skeleton based action recognition. Inspired by the
observation that the co-occurrences of the joints intrinsically characterize
human actions, we take the skeleton as the input at each time slot and
introduce a novel regularization scheme to learn the co-occurrence features of
skeleton joints. To train the deep LSTM network effectively, we propose a new
dropout algorithm which simultaneously operates on the gates, cells, and output
responses of the LSTM neurons. Experimental results on three human action
recognition datasets consistently demonstrate the effectiveness of the proposed
model.Comment: AAAI 2016 conferenc
- …