569 research outputs found
Compressed sensing and robust recovery of low rank matrices
In this paper, we focus on compressed sensing and recovery schemes for low-rank matrices, asking under what conditions a low-rank matrix can be sensed and recovered from incomplete, inaccurate, and noisy observations. We consider three schemes, one based on a certain Restricted Isometry Property and two based on directly sensing the row and column space of the matrix. We study their properties in terms of exact recovery in the ideal case, and robustness issues for approximately low-rank matrices and for noisy measurements
Asynchronous Training of Word Embeddings for Large Text Corpora
Word embeddings are a powerful approach for analyzing language and have been
widely popular in numerous tasks in information retrieval and text mining.
Training embeddings over huge corpora is computationally expensive because the
input is typically sequentially processed and parameters are synchronously
updated. Distributed architectures for asynchronous training that have been
proposed either focus on scaling vocabulary sizes and dimensionality or suffer
from expensive synchronization latencies.
In this paper, we propose a scalable approach to train word embeddings by
partitioning the input space instead in order to scale to massive text corpora
while not sacrificing the performance of the embeddings. Our training procedure
does not involve any parameter synchronization except a final sub-model merge
phase that typically executes in a few minutes. Our distributed training scales
seamlessly to large corpus sizes and we get comparable and sometimes even up to
45% performance improvement in a variety of NLP benchmarks using models trained
by our distributed procedure which requires of the time taken by the
baseline approach. Finally we also show that we are robust to missing words in
sub-models and are able to effectively reconstruct word representations.Comment: This paper contains 9 pages and has been accepted in the WSDM201
BlinkML: Efficient Maximum Likelihood Estimation with Probabilistic Guarantees
The rising volume of datasets has made training machine learning (ML) models
a major computational cost in the enterprise. Given the iterative nature of
model and parameter tuning, many analysts use a small sample of their entire
data during their initial stage of analysis to make quick decisions (e.g., what
features or hyperparameters to use) and use the entire dataset only in later
stages (i.e., when they have converged to a specific model). This sampling,
however, is performed in an ad-hoc fashion. Most practitioners cannot precisely
capture the effect of sampling on the quality of their model, and eventually on
their decision-making process during the tuning phase. Moreover, without
systematic support for sampling operators, many optimizations and reuse
opportunities are lost.
In this paper, we introduce BlinkML, a system for fast, quality-guaranteed ML
training. BlinkML allows users to make error-computation tradeoffs: instead of
training a model on their full data (i.e., full model), BlinkML can quickly
train an approximate model with quality guarantees using a sample. The quality
guarantees ensure that, with high probability, the approximate model makes the
same predictions as the full model. BlinkML currently supports any ML model
that relies on maximum likelihood estimation (MLE), which includes Generalized
Linear Models (e.g., linear regression, logistic regression, max entropy
classifier, Poisson regression) as well as PPCA (Probabilistic Principal
Component Analysis). Our experiments show that BlinkML can speed up the
training of large-scale ML tasks by 6.26x-629x while guaranteeing the same
predictions, with 95% probability, as the full model.Comment: 22 pages, SIGMOD 201
Ab initio study of the vapour-liquid critical point of a symmetrical binary fluid mixture
A microscopic approach to the investigation of the behaviour of a symmetrical
binary fluid mixture in the vicinity of the vapour-liquid critical point is
proposed. It is shown that the problem can be reduced to the calculation of the
partition function of a 3D Ising model in an external field. For a square-well
symmetrical binary mixture we calculate the parameters of the critical point as
functions of the microscopic parameter r measuring the relative strength of
interactions between the particles of dissimilar and similar species. The
calculations are performed at intermediate () and moderately long
() intermolecular potential ranges. The obtained results agree
well with the ones of computer simulations.Comment: 14 pages, Latex2e, 5 eps-figures included, submitted to
J.Phys:Cond.Ma
Estimation in high dimensions: a geometric perspective
This tutorial provides an exposition of a flexible geometric framework for
high dimensional estimation problems with constraints. The tutorial develops
geometric intuition about high dimensional sets, justifies it with some results
of asymptotic convex geometry, and demonstrates connections between geometric
results and estimation problems. The theory is illustrated with applications to
sparse recovery, matrix completion, quantization, linear and logistic
regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change
Axillary recurrences after sentinel node (SLN) biopsy without complete axillary dissection in breast cancer patients
Sequencing chemotherapy and radiotherapy in locoregional advanced breast cancer patients after mastectomy – a retrospective analysis
<p>Abstract</p> <p>Background</p> <p>Combined chemo- and radiotherapy are established in breast cancer treatment. Chemotherapy is recommended prior to radiotherapy but decisive data on the optimal sequence are rare. This retrospective analysis aimed to assess the role of sequencing in patients after mastectomy because of advanced locoregional disease.</p> <p>Methods</p> <p>A total of 212 eligible patients had a stage III breast cancer and had adjuvant chemotherapy and radiotherapy after mastectomy and axillary dissection between 1996 and 2004. According to concerted multi-modality treatment strategies 86 patients were treated sequentially (chemotherapy followed by radiotherapy) (SEQgroup), 70 patients had a sandwich treatment (SW-group) and 56 patients had simultaneous chemoradiation (SIM-group) during that time period. Radiotherapy comprised the thoracic wall and/or regional lymph nodes. The total dose was 45–50.4 Gray. As simultaneous chemoradiation CMF was given in 95.4% of patients while in sequential or sandwich application in 86% and 87.1% of patients an anthracycline-based chemotherapy was given.</p> <p>Results</p> <p>Concerning the parameters nodal involvement, lymphovascular invasion, extracapsular spread and extension of the irradiated region the three treatment groups were significantly imbalanced. The other parameters, e.g. age, pathological tumor stage, grading and receptor status were homogeneously distributed. Looking on those two groups with an equally effective chemotherapy (EC, FEC), the SEQ- and SW-group, the sole imbalance was the extension of LVI (57.1 vs. 25.6%, p < 0.0001).</p> <p>5-year overall- and disease free survival were 53.2%/56%, 38.1%/32% and 64.2%/50%, for the sequential, sandwich and simultaneous regime, respectively, which differed significantly in the univariate analysis (p = 0.04 and p = 0.03, log-rank test). Also the 5-year locoregional or distant recurrence free survival showed no significant differences according to the sequence of chemo- and radiotherapy. In the multivariate analyses the sequence had no independent impact on overall survival (p = 0.2) or disease free survival (p = 0.4). The toxicity, whether acute nor late, showed no significant differences in the three groups. The grade III/IV acute side effects were 3.6%, 0% and 3.5% for the SIM-, SW- and SEQ-group. By tendency the SIM regime had more late side effects.</p> <p>Conclusion</p> <p>No clear advantage can be stated for any radio- and chemotherapy sequence in breast cancer therapy so far. This could be confirmed in our retrospective analysis in high-risk patients after mastectomy. The sequential approach is recommended according to current guidelines considering a lower toxicity.</p
Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators
Intuitively, if a density operator has small rank, then it should be easier
to estimate from experimental data, since in this case only a few eigenvectors
need to be learned. We prove two complementary results that confirm this
intuition. First, we show that a low-rank density matrix can be estimated using
fewer copies of the state, i.e., the sample complexity of tomography decreases
with the rank. Second, we show that unknown low-rank states can be
reconstructed from an incomplete set of measurements, using techniques from
compressed sensing and matrix completion. These techniques use simple Pauli
measurements, and their output can be certified without making any assumptions
about the unknown state.
We give a new theoretical analysis of compressed tomography, based on the
restricted isometry property (RIP) for low-rank matrices. Using these tools, we
obtain near-optimal error bounds, for the realistic situation where the data
contains noise due to finite statistics, and the density matrix is full-rank
with decaying eigenvalues. We also obtain upper-bounds on the sample complexity
of compressed tomography, and almost-matching lower bounds on the sample
complexity of any procedure using adaptive sequences of Pauli measurements.
Using numerical simulations, we compare the performance of two compressed
sensing estimators with standard maximum-likelihood estimation (MLE). We find
that, given comparable experimental resources, the compressed sensing
estimators consistently produce higher-fidelity state reconstructions than MLE.
In addition, the use of an incomplete set of measurements leads to faster
classical processing with no loss of accuracy.
Finally, we show how to certify the accuracy of a low rank estimate using
direct fidelity estimation and we describe a method for compressed quantum
process tomography that works for processes with small Kraus rank.Comment: 16 pages, 3 figures. Matlab code included with the source file
Robust Matrix Completion
This paper considers the problem of recovery of a low-rank matrix in the
situation when most of its entries are not observed and a fraction of observed
entries are corrupted. The observations are noisy realizations of the sum of a
low rank matrix, which we wish to recover, with a second matrix having a
complementary sparse structure such as element-wise or column-wise sparsity. We
analyze a class of estimators obtained by solving a constrained convex
optimization problem that combines the nuclear norm and a convex relaxation for
a sparse constraint. Our results are obtained for the simultaneous presence of
random and deterministic patterns in the sampling scheme. We provide guarantees
for recovery of low-rank and sparse components from partial and corrupted
observations in the presence of noise and show that the obtained rates of
convergence are minimax optimal
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