22,828 research outputs found
Differentially private partitioned variational inference
Learning a privacy-preserving model from sensitive data which are distributed
across multiple devices is an increasingly important problem. The problem is
often formulated in the federated learning context, with the aim of learning a
single global model while keeping the data distributed. Moreover, Bayesian
learning is a popular approach for modelling, since it naturally supports
reliable uncertainty estimates. However, Bayesian learning is generally
intractable even with centralised non-private data and so approximation
techniques such as variational inference are a necessity. Variational inference
has recently been extended to the non-private federated learning setting via
the partitioned variational inference algorithm. For privacy protection, the
current gold standard is called differential privacy. Differential privacy
guarantees privacy in a strong, mathematically clearly defined sense.
In this paper, we present differentially private partitioned variational
inference, the first general framework for learning a variational approximation
to a Bayesian posterior distribution in the federated learning setting while
minimising the number of communication rounds and providing differential
privacy guarantees for data subjects.
We propose three alternative implementations in the general framework, one
based on perturbing local optimisation runs done by individual parties, and two
based on perturbing updates to the global model (one using a version of
federated averaging, the second one adding virtual parties to the protocol),
and compare their properties both theoretically and empirically.Comment: Published in TMLR 04/2023: https://openreview.net/forum?id=55Bcghgic
A spatio-temporal framework for modelling wastewater concentration during the COVID-19 pandemic
The potential utility of wastewater-based epidemiology as an early warning tool has been explored widely across the globe during the current COVID-19 pandemic. Methods to detect the presence of SARS-CoV-2 RNA in wastewater were developed early in the pandemic, and extensive work has been conducted to evaluate the relationship between viral concentration and COVID-19 case numbers at the catchment areas of sewage treatment works (STWs) over time. However, no attempt has been made to develop a model that predicts wastewater concentration at fine spatio-temporal resolutions covering an entire country, a necessary step towards using wastewater monitoring for the early detection of local outbreaks. We consider weekly averages of flow-normalised viral concentration, reported as the number of SARS-CoV-2N1 gene copies per litre (gc/L) of wastewater available at 303 STWs over the period between 1 June 2021 and 30 March 2022. We specify a spatially continuous statistical model that quantifies the relationship between weekly viral concentration and a collection of covariates covering socio-demographics, land cover and virus associated genomic characteristics at STW catchment areas while accounting for spatial and temporal correlation. We evaluate the model’s predictive performance at the catchment level through 10-fold cross-validation. We predict the weekly viral concentration at the population-weighted centroid of the 32,844 lower super output areas (LSOAs) in England, then aggregate these LSOA predictions to the Lower Tier Local Authority level (LTLA), a geography that is more relevant to public health policy-making. We also use the model outputs to quantify the probability of local changes of direction (increases or decreases) in viral concentration over short periods (e.g. two consecutive weeks). The proposed statistical framework can predict SARS-CoV-2 viral concentration in wastewater at high spatio-temporal resolution across England. Additionally, the probabilistic quantification of local changes can be used as an early warning tool for public health surveillance
Statistical phase estimation and error mitigation on a superconducting quantum processor
Quantum phase estimation (QPE) is a key quantum algorithm, which has been
widely studied as a method to perform chemistry and solid-state calculations on
future fault-tolerant quantum computers. Recently, several authors have
proposed statistical alternatives to QPE that have benefits on early
fault-tolerant devices, including shorter circuits and better suitability for
error mitigation techniques. However, practical implementations of the
algorithm on real quantum processors are lacking. In this paper we practically
implement statistical phase estimation on Rigetti's superconducting processors.
We specifically use the method of Lin and Tong [PRX Quantum 3, 010318 (2022)]
using the improved Fourier approximation of Wan et al. [PRL 129, 030503
(2022)], and applying a variational compilation technique to reduce circuit
depth. We then incorporate error mitigation strategies including zero-noise
extrapolation and readout error mitigation with bit-flip averaging. We propose
a simple method to estimate energies from the statistical phase estimation
data, which is found to improve the accuracy in final energy estimates by one
to two orders of magnitude with respect to prior theoretical bounds, reducing
the cost to perform accurate phase estimation calculations. We apply these
methods to chemistry problems for active spaces up to 4 electrons in 4
orbitals, including the application of a quantum embedding method, and use them
to correctly estimate energies within chemical precision. Our work demonstrates
that statistical phase estimation has a natural resilience to noise,
particularly after mitigating coherent errors, and can achieve far higher
accuracy than suggested by previous analysis, demonstrating its potential as a
valuable quantum algorithm for early fault-tolerant devices.Comment: 24 pages, 13 figure
Examples of works to practice staccato technique in clarinet instrument
Klarnetin staccato tekniğini güçlendirme aşamaları eser çalışmalarıyla uygulanmıştır. Staccato
geçişlerini hızlandıracak ritim ve nüans çalışmalarına yer verilmiştir. Çalışmanın en önemli amacı
sadece staccato çalışması değil parmak-dilin eş zamanlı uyumunun hassasiyeti üzerinde de
durulmasıdır. Staccato çalışmalarını daha verimli hale getirmek için eser çalışmasının içinde etüt
çalışmasına da yer verilmiştir. Çalışmaların üzerinde titizlikle durulması staccato çalışmasının ilham
verici etkisi ile müzikal kimliğe yeni bir boyut kazandırmıştır. Sekiz özgün eser çalışmasının her
aşaması anlatılmıştır. Her aşamanın bir sonraki performans ve tekniği güçlendirmesi esas alınmıştır.
Bu çalışmada staccato tekniğinin hangi alanlarda kullanıldığı, nasıl sonuçlar elde edildiği bilgisine
yer verilmiştir. Notaların parmak ve dil uyumu ile nasıl şekilleneceği ve nasıl bir çalışma disiplini
içinde gerçekleşeceği planlanmıştır. Kamış-nota-diyafram-parmak-dil-nüans ve disiplin
kavramlarının staccato tekniğinde ayrılmaz bir bütün olduğu saptanmıştır. Araştırmada literatür
taraması yapılarak staccato ile ilgili çalışmalar taranmıştır. Tarama sonucunda klarnet tekniğin de
kullanılan staccato eser çalışmasının az olduğu tespit edilmiştir. Metot taramasında da etüt
çalışmasının daha çok olduğu saptanmıştır. Böylelikle klarnetin staccato tekniğini hızlandırma ve
güçlendirme çalışmaları sunulmuştur. Staccato etüt çalışmaları yapılırken, araya eser çalışmasının
girmesi beyni rahatlattığı ve istekliliği daha arttırdığı gözlemlenmiştir. Staccato çalışmasını yaparken
doğru bir kamış seçimi üzerinde de durulmuştur. Staccato tekniğini doğru çalışmak için doğru bir
kamışın dil hızını arttırdığı saptanmıştır. Doğru bir kamış seçimi kamıştan rahat ses çıkmasına
bağlıdır. Kamış, dil atma gücünü vermiyorsa daha doğru bir kamış seçiminin yapılması gerekliliği
vurgulanmıştır. Staccato çalışmalarında baştan sona bir eseri yorumlamak zor olabilir. Bu açıdan
çalışma, verilen müzikal nüanslara uymanın, dil atış performansını rahatlattığını ortaya koymuştur.
Gelecek nesillere edinilen bilgi ve birikimlerin aktarılması ve geliştirici olması teşvik edilmiştir.
Çıkacak eserlerin nasıl çözüleceği, staccato tekniğinin nasıl üstesinden gelinebileceği anlatılmıştır.
Staccato tekniğinin daha kısa sürede çözüme kavuşturulması amaç edinilmiştir. Parmakların
yerlerini öğrettiğimiz kadar belleğimize de çalışmaların kaydedilmesi önemlidir. Gösterilen azmin ve
sabrın sonucu olarak ortaya çıkan yapıt başarıyı daha da yukarı seviyelere çıkaracaktır
Dual dynamic programming for stochastic programs over an infinite horizon
We consider a dual dynamic programming algorithm for solving stochastic
programs over an infinite horizon. We show non-asymptotic convergence results
when using an explorative strategy, and we then enhance this result by reducing
the dependence of the effective planning horizon from quadratic to linear. This
improvement is achieved by combining the forward and backward phases from dual
dynamic programming into a single iteration. We then apply our algorithms to a
class of problems called hierarchical stationary stochastic programs, where the
cost function is a stochastic multi-stage program. The hierarchical program can
model problems with a hierarchy of decision-making, e.g., how long-term
decisions influence day-to-day operations. We show that when the subproblems
are solved inexactly via a dynamic stochastic approximation-type method, the
resulting hierarchical dual dynamic programming can find approximately optimal
solutions in finite time. Preliminary numerical results show the practical
benefits of using the explorative strategy for solving the Brazilian
hydro-thermal planning problem and economic dispatch, as well as the potential
to exploit parallel computing.Comment: 45 pages. New experiments for hierarchical problem and writing
update
Single Image Depth Prediction Made Better: A Multivariate Gaussian Take
Neural-network-based single image depth prediction (SIDP) is a challenging
task where the goal is to predict the scene's per-pixel depth at test time.
Since the problem, by definition, is ill-posed, the fundamental goal is to come
up with an approach that can reliably model the scene depth from a set of
training examples. In the pursuit of perfect depth estimation, most existing
state-of-the-art learning techniques predict a single scalar depth value
per-pixel. Yet, it is well-known that the trained model has accuracy limits and
can predict imprecise depth. Therefore, an SIDP approach must be mindful of the
expected depth variations in the model's prediction at test time. Accordingly,
we introduce an approach that performs continuous modeling of per-pixel depth,
where we can predict and reason about the per-pixel depth and its distribution.
To this end, we model per-pixel scene depth using a multivariate Gaussian
distribution. Moreover, contrary to the existing uncertainty modeling methods
-- in the same spirit, where per-pixel depth is assumed to be independent, we
introduce per-pixel covariance modeling that encodes its depth dependency w.r.t
all the scene points. Unfortunately, per-pixel depth covariance modeling leads
to a computationally expensive continuous loss function, which we solve
efficiently using the learned low-rank approximation of the overall covariance
matrix. Notably, when tested on benchmark datasets such as KITTI, NYU, and
SUN-RGB-D, the SIDP model obtained by optimizing our loss function shows
state-of-the-art results. Our method's accuracy (named MG) is among the top on
the KITTI depth-prediction benchmark leaderboard.Comment: Accepted to IEEE/CVF CVPR 2023. Draft info: 17 pages, 13 Figures, 9
Table
Dynamic Subspace Estimation with Grassmannian Geodesics
Dynamic subspace estimation, or subspace tracking, is a fundamental problem
in statistical signal processing and machine learning. This paper considers a
geodesic model for time-varying subspaces. The natural objective function for
this model is non-convex. We propose a novel algorithm for minimizing this
objective and estimating the parameters of the model from data with
Grassmannian-constrained optimization. We show that with this algorithm, the
objective is monotonically non-increasing. We demonstrate the performance of
this model and our algorithm on synthetic data, video data, and dynamic fMRI
data
DiffRF: Rendering-Guided 3D Radiance Field Diffusion
We introduce DiffRF, a novel approach for 3D radiance field synthesis based
on denoising diffusion probabilistic models. While existing diffusion-based
methods operate on images, latent codes, or point cloud data, we are the first
to directly generate volumetric radiance fields. To this end, we propose a 3D
denoising model which directly operates on an explicit voxel grid
representation. However, as radiance fields generated from a set of posed
images can be ambiguous and contain artifacts, obtaining ground truth radiance
field samples is non-trivial. We address this challenge by pairing the
denoising formulation with a rendering loss, enabling our model to learn a
deviated prior that favours good image quality instead of trying to replicate
fitting errors like floating artifacts. In contrast to 2D-diffusion models, our
model learns multi-view consistent priors, enabling free-view synthesis and
accurate shape generation. Compared to 3D GANs, our diffusion-based approach
naturally enables conditional generation such as masked completion or
single-view 3D synthesis at inference time.Comment: Project page: https://sirwyver.github.io/DiffRF/ Video:
https://youtu.be/qETBcLu8SUk - CVPR 2023 Highlight - updated evaluations
after fixing initial data mapping error on all method
PreFair: Privately Generating Justifiably Fair Synthetic Data
When a database is protected by Differential Privacy (DP), its usability is
limited in scope. In this scenario, generating a synthetic version of the data
that mimics the properties of the private data allows users to perform any
operation on the synthetic data, while maintaining the privacy of the original
data. Therefore, multiple works have been devoted to devising systems for DP
synthetic data generation. However, such systems may preserve or even magnify
properties of the data that make it unfair, endering the synthetic data unfit
for use. In this work, we present PreFair, a system that allows for DP fair
synthetic data generation. PreFair extends the state-of-the-art DP data
generation mechanisms by incorporating a causal fairness criterion that ensures
fair synthetic data. We adapt the notion of justifiable fairness to fit the
synthetic data generation scenario. We further study the problem of generating
DP fair synthetic data, showing its intractability and designing algorithms
that are optimal under certain assumptions. We also provide an extensive
experimental evaluation, showing that PreFair generates synthetic data that is
significantly fairer than the data generated by leading DP data generation
mechanisms, while remaining faithful to the private data.Comment: 15 pages, 11 figure
A variational Bayesian inference technique for model updating of structural systems with unknown noise statistics
Dynamic models of structural and mechanical systems can be updated to match the measured data through a Bayesian inference process. However, the performance of classical (non-adaptive) Bayesian model updating approaches decreases significantly when the pre-assumed statistical characteristics of the model prediction error are violated. To overcome this issue, this paper presents an adaptive recursive variational Bayesian approach to estimate the statistical characteristics of the prediction error jointly with the unknown model parameters. This approach improves the accuracy and robustness of model updating by including the estimation of model prediction error. The performance of this approach is demonstrated using numerically simulated data obtained from a structural frame with material non-linearity under earthquake excitation. Results show that in the presence of non-stationary noise/error, the non-adaptive approach fails to estimate unknown model parameters, whereas the proposed approach can accurately estimate them
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