1,184 research outputs found
Logistic Regression: Tight Bounds for Stochastic and Online Optimization
The logistic loss function is often advocated in machine learning and
statistics as a smooth and strictly convex surrogate for the 0-1 loss. In this
paper we investigate the question of whether these smoothness and convexity
properties make the logistic loss preferable to other widely considered options
such as the hinge loss. We show that in contrast to known asymptotic bounds, as
long as the number of prediction/optimization iterations is sub exponential,
the logistic loss provides no improvement over a generic non-smooth loss
function such as the hinge loss. In particular we show that the convergence
rate of stochastic logistic optimization is bounded from below by a polynomial
in the diameter of the decision set and the number of prediction iterations,
and provide a matching tight upper bound. This resolves the COLT open problem
of McMahan and Streeter (2012)
Beyond Convexity: Stochastic Quasi-Convex Optimization
Stochastic convex optimization is a basic and well studied primitive in
machine learning. It is well known that convex and Lipschitz functions can be
minimized efficiently using Stochastic Gradient Descent (SGD). The Normalized
Gradient Descent (NGD) algorithm, is an adaptation of Gradient Descent, which
updates according to the direction of the gradients, rather than the gradients
themselves. In this paper we analyze a stochastic version of NGD and prove its
convergence to a global minimum for a wider class of functions: we require the
functions to be quasi-convex and locally-Lipschitz. Quasi-convexity broadens
the con- cept of unimodality to multidimensions and allows for certain types of
saddle points, which are a known hurdle for first-order optimization methods
such as gradient descent. Locally-Lipschitz functions are only required to be
Lipschitz in a small region around the optimum. This assumption circumvents
gradient explosion, which is another known hurdle for gradient descent
variants. Interestingly, unlike the vanilla SGD algorithm, the stochastic
normalized gradient descent algorithm provably requires a minimal minibatch
size
On Graduated Optimization for Stochastic Non-Convex Problems
The graduated optimization approach, also known as the continuation method,
is a popular heuristic to solving non-convex problems that has received renewed
interest over the last decade. Despite its popularity, very little is known in
terms of theoretical convergence analysis. In this paper we describe a new
first-order algorithm based on graduated optimiza- tion and analyze its
performance. We characterize a parameterized family of non- convex functions
for which this algorithm provably converges to a global optimum. In particular,
we prove that the algorithm converges to an {\epsilon}-approximate solution
within O(1/\epsilon^2) gradient-based steps. We extend our algorithm and
analysis to the setting of stochastic non-convex optimization with noisy
gradient feedback, attaining the same convergence rate. Additionally, we
discuss the setting of zero-order optimization, and devise a a variant of our
algorithm which converges at rate of O(d^2/\epsilon^4).Comment: 17 page
Optimal Rates for Bandit Nonstochastic Control
Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) control
are foundational and extensively researched problems in optimal control. We
investigate LQR and LQG problems with semi-adversarial perturbations and
time-varying adversarial bandit loss functions. The best-known sublinear regret
algorithm of~\cite{gradu2020non} has a time horizon
dependence, and its authors posed an open question about whether a tight rate
of could be achieved. We answer in the affirmative, giving an
algorithm for bandit LQR and LQG which attains optimal regret (up to
logarithmic factors) for both known and unknown systems. A central component of
our method is a new scheme for bandit convex optimization with memory, which is
of independent interest
Contextual-based Image Inpainting: Infer, Match, and Translate
We study the task of image inpainting, which is to fill in the missing region
of an incomplete image with plausible contents. To this end, we propose a
learning-based approach to generate visually coherent completion given a
high-resolution image with missing components. In order to overcome the
difficulty to directly learn the distribution of high-dimensional image data,
we divide the task into inference and translation as two separate steps and
model each step with a deep neural network. We also use simple heuristics to
guide the propagation of local textures from the boundary to the hole. We show
that, by using such techniques, inpainting reduces to the problem of learning
two image-feature translation functions in much smaller space and hence easier
to train. We evaluate our method on several public datasets and show that we
generate results of better visual quality than previous state-of-the-art
methods.Comment: ECCV 2018 camera read
A Research and Strategy of Remote Sensing Image Denoising Algorithms
Most raw data download from satellites are useless, resulting in transmission
waste, one solution is to process data directly on satellites, then only
transmit the processed results to the ground. Image processing is the main data
processing on satellites, in this paper, we focus on image denoising which is
the basic image processing. There are many high-performance denoising
approaches at present, however, most of them rely on advanced computing
resources or rich images on the ground. Considering the limited computing
resources of satellites and the characteristics of remote sensing images, we do
some research on these high-performance ground image denoising approaches and
compare them in simulation experiments to analyze whether they are suitable for
satellites. According to the analysis results, we propose two feasible image
denoising strategies for satellites based on satellite TianZhi-1.Comment: 9 pages, 4 figures, ICNC-FSKD 201
Complex-valued Retrievals From Noisy Images Using Diffusion Models
In diverse microscopy modalities, sensors measure only real-valued
intensities. Additionally, the sensor readouts are affected by
Poissonian-distributed photon noise. Traditional restoration algorithms
typically aim to minimize the mean squared error (MSE) between the original and
recovered images. This often leads to blurry outcomes with poor perceptual
quality. Recently, deep diffusion models (DDMs) have proven to be highly
capable of sampling images from the a-posteriori probability of the sought
variables, resulting in visually pleasing high-quality images. These models
have mostly been suggested for real-valued images suffering from Gaussian
noise. In this study, we generalize annealed Langevin Dynamics, a type of DDM,
to tackle the fundamental challenges in optical imaging of complex-valued
objects (and real images) affected by Poisson noise. We apply our algorithm to
various optical scenarios, such as Fourier Ptychography, Phase Retrieval, and
Poisson denoising. Our algorithm is evaluated on simulations and biological
empirical data.Comment: 11 pages, 7figure
Multiple breast cancer risk variants are associated with differential transcript isoform expression in tumors.
Genome-wide association studies have identified over 70 single-nucleotide polymorphisms (SNPs) associated with breast cancer. A subset of these SNPs are associated with quantitative expression of nearby genes, but the functional effects of the majority remain unknown. We hypothesized that some risk SNPs may regulate alternative splicing. Using RNA-sequencing data from breast tumors and germline genotypes from The Cancer Genome Atlas, we tested the association between each risk SNP genotype and exon-, exon-exon junction- or transcript-specific expression of nearby genes. Six SNPs were associated with differential transcript expression of seven nearby genes at FDR < 0.05 (BABAM1, DCLRE1B/PHTF1, PEX14, RAD51L1, SRGAP2D and STXBP4). We next developed a Bayesian approach to evaluate, for each SNP, the overlap between the signal of association with breast cancer and the signal of association with alternative splicing. At one locus (SRGAP2D), this method eliminated the possibility that the breast cancer risk and the alternate splicing event were due to the same causal SNP. Lastly, at two loci, we identified the likely causal SNP for the alternative splicing event, and at one, functionally validated the effect of that SNP on alternative splicing using a minigene reporter assay. Our results suggest that the regulation of differential transcript isoform expression is the functional mechanism of some breast cancer risk SNPs and that we can use these associations to identify causal SNPs, target genes and the specific transcripts that may mediate breast cancer risk
Mathematical Modeling of a Bioluminescent E. Coli Based Biosensor
In this work we present a mathematical model for the bioreporter activity of an E. coli based bioluminescent bioreporter. This bioreporter is based on a genetically modified E. coli which harbors the recA promoter, a member of the bacterial SOS response, fused to the bacterial luminescence (lux) genes. This bioreporter responds to the presence of DNA damaging agents such as heavy metals, H2O2 and Nalidixic Acid (NA) that activate the SOS response. In our mathematical model we implemented basic physiological mechanisms such as: the penetration of the NA into the biosensor; gyrase enzyme inhibition by the NA; gyrase level regulation; creation of chromosomal DNA damage; DNA repair and release of ssDNA into the cytoplasm; SOS induction and chromosomal DNA repair; activation of lux genes by the fused recA promoter carried on a plasmidal DNA; transcription and translation of the luminescence responsible enzymes; luminescence cycle; energy molecules level regulation and the regulation of the O2 consumption.
The mathematical model was defined using a set of ordinary differential equations (ODE) and solved numerically. We simulated the system for different concentrations of NA in water for specific biosensors concentration, and under limited O2 conditions. The simulated results were compared to experimental data and satisfactory matching was obtained. This manuscript presents a proof of concept showing that real biosensors can be modeled and simulated. This sets the ground to the next stage of implementing a comprehensive physiological model using experimentally extracted parameters. Following the completion of the next stage, it will be possible to construct a “Computer Aided Design” tool for the simulation of the genetically engineered biosensors. We define a term “bioCAD” for a Biological System Computer Aided Design. The specific bioCAD that is described here is aimed towards whole cell biosensors which are under investigation today for functional sensing. Usage of the bioCAD will improve the biosensors design process and boost their performance. It will also reduce Non Recurring Engineering (NRE) cost and time. Finally, using a parameterized solution will allow fair and quick evaluation of whole cell biosensors for various applications
Sparsity and cosparsity for audio declipping: a flexible non-convex approach
This work investigates the empirical performance of the sparse synthesis
versus sparse analysis regularization for the ill-posed inverse problem of
audio declipping. We develop a versatile non-convex heuristics which can be
readily used with both data models. Based on this algorithm, we report that, in
most cases, the two models perform almost similarly in terms of signal
enhancement. However, the analysis version is shown to be amenable for real
time audio processing, when certain analysis operators are considered. Both
versions outperform state-of-the-art methods in the field, especially for the
severely saturated signals
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