IA Scholar Query: A Time-Optimal Parallel Algorithm for Three-Dimensional Convex Hulls.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgSat, 31 Dec 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440A Survey on Concept Drift in Process Mining
https://scholar.archive.org/work/hvmkupdorzf5df4tts42gzykjm
Concept drift in process mining (PM) is a challenge as classical methods assume processes are in a steady-state, i.e., events share the same process version. We conducted a systematic literature review on the intersection of these areas, and thus, we review concept drift in PM and bring forward a taxonomy of existing techniques for drift detection and online PM for evolving environments. Existing works depict that (i) PM still primarily focuses on offline analysis, and (ii) the assessment of concept drift techniques in processes is cumbersome due to the lack of common evaluation protocol, datasets, and metrics.Denise Maria Vecino Sato, Sheila Cristiana De Freitas, Jean Paul Barddal, Edson Emilio Scalabrinwork_hvmkupdorzf5df4tts42gzykjmSat, 31 Dec 2022 00:00:00 GMTOn Finding Rank Regret Representatives
https://scholar.archive.org/work/r4npneviqrf5nludmsukxruju4
Selecting the best items in a dataset is a common task in data exploration. However, the concept of "best" lies in the eyes of the beholder: Different users may consider different attributes more important and, hence, arrive at different rankings. Nevertheless, one can remove "dominated" items and create a "representative" subset of the data, comprising the "best items" in it. A Pareto-optimal representative is guaranteed to contain the best item of each possible ranking, but it can be a large portion of data. A much smaller representative can be found if we relax the requirement of including the best item for each user and instead just limit the users' "regret." Existing work defines regret as the loss in score by limiting consideration to the representative instead of the full dataset, for any chosen ranking function. However, the score is often not a meaningful number, and users may not understand its absolute value. Sometimes small ranges in score can include large fractions of the dataset. In contrast, users do understand the notion of rank ordering. Therefore, we consider items' positions in the ranked list in defining the regret and propose the rank-regret representative as the minimal subset of the data containing at least one of the top- k of any possible ranking function. This problem is polynomial time solvable in two-dimensional space but is NP-hard on three or more dimensions. We design a suite of algorithms to fulfill different purposes, such as whether relaxation is permitted on k , the result size, or both, whether a distribution is known, whether theoretical guarantees or practical efficiency is important, and so on. Experiments on real datasets demonstrate that we can efficiently find small subsets with small rank-regrets.Abolfazl Asudeh, Gautam Das, H. V. Jagadish, Shangqi Lu, Azade Nazi, Yufei Tao, Nan Zhang, Jianwen Zhaowork_r4npneviqrf5nludmsukxruju4Fri, 30 Sep 2022 00:00:00 GMTPersuasion with Coarse Communication
https://scholar.archive.org/work/zpj57vhkujhc7auchlwyx5jati
How does an expert's ability persuade change with the availability of messages? We study games of Bayesian persuasion the sender is unable to fully describe every state of the world or recommend all possible actions. We characterize the set of attainable payoffs. Sender always does worse with coarse communication and values additional signals. We show that there exists an upper bound on the marginal value of a signal for the sender. In a special class of games, the marginal value of a signal is increasing when the receiver is difficult to persuade. We show that an additional signal does not directly translate into more information and the receiver might prefer coarse communication. Finally, we study the geometric properties of optimal information structures. Using these properties, we show that the sender's optimization problem can be solved by searching within a finite set.Yunus C. Aybas, Eray Turkelwork_zpj57vhkujhc7auchlwyx5jatiThu, 15 Sep 2022 00:00:00 GMTA tomographic spherical mass map emulator of the KiDS-1000 survey using conditional generative adversarial networks
https://scholar.archive.org/work/jwnwfbeu5ncxzjhuoj57sq43oe
Large sets of matter density simulations are becoming increasingly important in large scale structure cosmology. Matter power spectra emulators, such as the Euclid Emulator and CosmicEmu, are trained on simulations to correct the non-linear part of the power spectrum. Map-based analyses retrieve additional non-Gaussian information from the density field, whether through human-designed statistics such as peak counts, or via machine learning methods such as convolutional neural networks (CNNs). The simulations required for these methods are very resource-intensive, both in terms of computing time and storage. Map-level density field emulators, based on deep generative models, have recently been proposed to address these challenges. In this work, we present a novel mass map emulator of the KiDS-1000 survey footprint, which generates noise-free spherical maps in a fraction of a second. It takes a set of cosmological parameters (Ω_M, σ_8) as input and produces a consistent set of 5 maps, corresponding to the KiDS-1000 tomographic redshift bins. To construct the emulator, we use a conditional generative adversarial network architecture and the spherical CNN , and train it on N-body-simulated mass maps. We compare its performance using an array of quantitative comparison metrics: angular power spectra C_ℓ, pixel/peaks distributions, C_ℓ correlation matrices, and Structural Similarity Index. Overall, the agreement on these summary statistics is <10% for the cosmologies at the centre of the simulation grid, and degrades slightly on grid edges. Finally, we perform a mock cosmological parameter estimation using the emulator and the original simulation set. We find good agreement in these constraints, for both likelihood and likelihood-free approaches. The emulator is available at https://tfhub.dev/cosmo-group-ethz/models/kids-cgan/1.Timothy Wing Hei Yiu, Janis Fluri, Tomasz Kacprzakwork_jwnwfbeu5ncxzjhuoj57sq43oeThu, 15 Sep 2022 00:00:00 GMTReal-time intelligent classification of COVID-19 and thrombosis via massive image-based analysis of platelet aggregates
https://scholar.archive.org/work/qxhvciugy5b3vegvn3ky3hk56q
ABSTRACTMicrovascular thrombosis is a typical symptom of COVID-19 and shows similarities to thrombosis. Using a microfluidic imaging flow cytometer, we measured the blood of 181 COVID-19 samples and 101 non-COVID-19 thrombosis samples, resulting in a total of 6.3 million bright-field images. We trained a convolutional neural network to distinguish single platelets, platelet aggregates, and white blood cells and performed classical image analysis for each subpopulation individually. Based on derived single-cell features for each population, we trained machine learning models for classification between COVID-19 and non-COVID-19 thrombosis, resulting in a patient testing accuracy of 75%. This result indicates that platelet formation differs between COVID-19 and non-COVID-19 thrombosis. All analysis steps were optimized for efficiency and implemented in an easy-to-use plugin for the image viewer napari, allowing the entire analysis to be performed within seconds on mid-range computers, which could be used for real-time diagnosis.Chenqi Zhang, Maik Herbig, Yuqi Zhou, Masako Nishikawa, Mohammad Shifat-E-Rabbi, Hiroshi Kanno, Ruoxi Yang, Yuma Ibayashi, Ting-Hui Xiao, Gustavo K. Rohde, Masataka Sato, Satoshi Kodera, Masao Daimon, Yutaka Yatomi, Keisuke Godawork_qxhvciugy5b3vegvn3ky3hk56qThu, 15 Sep 2022 00:00:00 GMTCluster-based multidimensional scaling embedding tool for data visualization
https://scholar.archive.org/work/cyzdgt5e6vf6rcgmm7lvdjx4pu
We present a new technique for visualizing high-dimensional data called cluster MDS (cl-MDS), which addresses a common difficulty of dimensionality reduction methods: preserving both local and global structures of the original sample in a single 2-dimensional visualization. Its algorithm combines the well-known multidimensional scaling (MDS) tool with the k-medoids data clustering technique, and enables hierarchical embedding, sparsification and estimation of 2-dimensional coordinates for additional points. While cl-MDS is a generally applicable tool, we also include specific recipes for atomic structure applications. We apply this method to non-linear data of increasing complexity where different layers of locality are relevant, showing a clear improvement in their retrieval and visualization quality.Patricia Hernández-León, Miguel A. Carowork_cyzdgt5e6vf6rcgmm7lvdjx4puWed, 14 Sep 2022 00:00:00 GMTA Scalable and Energy Efficient GPU Thread Map for m-Simplex Domains
https://scholar.archive.org/work/oe7ew7zzqvb57hfobr3ig6bw7a
This work proposes a new GPU thread map for m-simplex domains, that scales its speedup with dimension and is energy efficient compared to other state of the art approaches. The main contributions of this work are i) the formulation of the new block-space map ℋ: ℤ^m ↦ℤ^m for regular orthogonal simplex domains, which is analyzed in terms of resource usage, and ii) the experimental evaluation in terms of speedup over a bounding box approach and energy efficiency as elements per second per Watt. Results from the analysis show that ℋ has a potential speedup of up to 2× and 6× for 2 and 3-simplices, respectively. Experimental evaluation shows that ℋ is competitive for 2-simplices, reaching 1.2×∼ 2.0× of speedup for different tests, which is on par with the fastest state of the art approaches. For 3-simplices ℋ reaches up to 1.3×∼ 6.0× of speedup making it the fastest of all. The extension of ℋ to higher dimensional m-simplices is feasible and has a potential speedup that scales as m! given a proper selection of parameters r, β which are the scaling and replication factors, respectively. In terms of energy consumption, although ℋ is among the highest in power consumption, it compensates by its short duration, making it one of the most energy efficient approaches. Lastly, further improvements with Tensor and Ray Tracing Cores are analyzed, giving insights to leverage each one of them. The results obtained in this work show that ℋ is a scalable and energy efficient map that can contribute to the efficiency of GPU applications when they need to process m-simplex domains, such as Cellular Automata or PDE simulations.Cristóbal A. Navarro, Felipe A. Quezada, Benjamin Bustos, Nancy Hitschfeld, Rolando Kindelanwork_oe7ew7zzqvb57hfobr3ig6bw7aMon, 12 Sep 2022 00:00:00 GMTScalable Distributed Optimization of Multi-Dimensional Functions Despite Byzantine Adversaries
https://scholar.archive.org/work/cfucczwnmjcdlkpjsnhqfp366e
The problem of distributed optimization requires a group of networked agents to compute a parameter that minimizes the average of their local cost functions. While there are a variety of distributed optimization algorithms that can solve this problem, they are typically vulnerable to "Byzantine" agents that do not follow the algorithm. Recent attempts to address this issue focus on single dimensional functions, or assume certain statistical properties of the functions at the agents. In this paper, we provide two resilient, scalable, distributed optimization algorithms for multi-dimensional functions. Our schemes involve two filters, (1) a distance-based filter and (2) a min-max filter, which each remove neighborhood states that are extreme (defined precisely in our algorithms) at each iteration. We show that these algorithms can mitigate the impact of up to F (unknown) Byzantine agents in the neighborhood of each regular agent. In particular, we show that if the network topology satisfies certain conditions, all of the regular agents' states are guaranteed to converge to a bounded region that contains the minimizer of the average of the regular agents' functions.Kananart Kuwaranancharoen, Lei Xin, Shreyas Sundaramwork_cfucczwnmjcdlkpjsnhqfp366eMon, 12 Sep 2022 00:00:00 GMTEvading the Simplicity Bias: Training a Diverse Set of Models Discovers Solutions with Superior OOD Generalization
https://scholar.archive.org/work/6mk56yrntjfafdypu7chpsgc24
Neural networks trained with SGD were recently shown to rely preferentially on linearly-predictive features and can ignore complex, equally-predictive ones. This simplicity bias can explain their lack of robustness out of distribution (OOD). The more complex the task to learn, the more likely it is that statistical artifacts (i.e. selection biases, spurious correlations) are simpler than the mechanisms to learn. We demonstrate that the simplicity bias can be mitigated and OOD generalization improved. We train a set of similar models to fit the data in different ways using a penalty on the alignment of their input gradients. We show theoretically and empirically that this induces the learning of more complex predictive patterns. OOD generalization fundamentally requires information beyond i.i.d. examples, such as multiple training environments, counterfactual examples, or other side information. Our approach shows that we can defer this requirement to an independent model selection stage. We obtain SOTA results in visual recognition on biased data and generalization across visual domains. The method - the first to evade the simplicity bias - highlights the need for a better understanding and control of inductive biases in deep learning.Damien Teney, Ehsan Abbasnejad, Simon Lucey, Anton van den Hengelwork_6mk56yrntjfafdypu7chpsgc24Sun, 11 Sep 2022 00:00:00 GMTParallel MCMC Algorithms: Theoretical Foundations, Algorithm Design, Case Studies
https://scholar.archive.org/work/3umk7mptarh33jr5jqkilcqhk4
Parallel Markov Chain Monte Carlo (pMCMC) algorithms generate clouds of proposals at each step to efficiently resolve a target probability distribution. We build a rigorous foundational framework for pMCMC algorithms that situates these methods within a unified 'extended phase space' measure-theoretic formalism. Drawing on our recent work that provides a comprehensive theory for reversible single proposal methods, we herein derive general criteria for multiproposal acceptance mechanisms which yield unbiased chains on general state spaces. Our formulation encompasses a variety of methodologies, including proposal cloud resampling and Hamiltonian methods, while providing a basis for the derivation of novel algorithms. In particular, we obtain a top-down picture for a class of methods arising from 'conditionally independent' proposal structures. As an immediate application, we identify several new algorithms including a multiproposal version of the popular preconditioned Crank-Nicolson (pCN) sampler suitable for high- and infinite-dimensional target measures which are absolutely continuous with respect to a Gaussian base measure. To supplement our theoretical results, we carry out a selection of numerical case studies that evaluate the efficacy of these novel algorithms. First, noting that the true potential of pMCMC algorithms arises from their natural parallelizability, we provide a limited parallelization study using TensorFlow and a graphics processing unit to scale pMCMC algorithms that leverage as many as 100k proposals at each step. Second, we use our multiproposal pCN algorithm (mpCN) to resolve a selection of problems in Bayesian statistical inversion for partial differential equations motivated by fluid measurement. These examples provide preliminary evidence of the efficacy of mpCN for high-dimensional target distributions featuring complex geometries and multimodal structures.Nathan E. Glatt-Holtz, Andrew J. Holbrook, Justin A. Krometis, Cecilia F. Mondainiwork_3umk7mptarh33jr5jqkilcqhk4Sat, 10 Sep 2022 00:00:00 GMTFinding the Optimal Dynamic Treatment Regime Using Smooth Fisher Consistent Surrogate Loss
https://scholar.archive.org/work/k2qzlz2vljgq3mdqpl2u5kkijm
Large health care data repositories such as electronic health records (EHR) opens new opportunities to derive individualized treatment strategies to improve disease outcomes. We study the problem of estimating sequential treatment rules tailored to patient's individual characteristics, often referred to as dynamic treatment regimes (DTRs). We seek to find the optimal DTR which maximizes the discontinuous value function through direct maximization of a fisher consistent surrogate loss function. We show that a large class of concave surrogates fails to be Fisher consistent, which differs from the classic setting for binary classification. We further characterize a non-concave family of Fisher consistent smooth surrogate functions, which can be optimized with gradient descent using off-the-shelf machine learning algorithms. Compared to the existing direct search approach under the support vector machine framework (Zhao et al., 2015), our proposed DTR estimation via surrogate loss optimization (DTRESLO) method is more computationally scalable to large sample size and allows for a broader functional class for the predictor effects. We establish theoretical properties for our proposed DTR estimator and obtain a sharp upper bound on the regret corresponding to our DTRESLO method. Finite sample performance of our proposed estimator is evaluated through extensive simulations and an application on deriving an optimal DTR for treatment sepsis using EHR data from patients admitted to intensive care units.Nilanjana Laha, Aaron Sonabend-W, Rajarshi Mukherjee, Tianxi Caiwork_k2qzlz2vljgq3mdqpl2u5kkijmSat, 10 Sep 2022 00:00:00 GMTA Unifying Approach to Efficient (Near)-Gathering of Disoriented Robots with Limited Visibility
https://scholar.archive.org/work/mwvpmikhsjd2tiii6fbygstcbu
We consider a swarm of n robots in ℝ^d. The robots are oblivious, disoriented (no common coordinate system/compass), and have limited visibility (observe other robots up to a constant distance). The basic formation task gathering requires that all robots reach the same, not predefined position. In the related near-gathering task, they must reach distinct positions such that every robot sees the entire swarm. In the considered setting, gathering can be solved in 𝒪(n + Δ^2) synchronous rounds both in two and three dimensions, where Δ denotes the initial maximal distance of two robots. In this work, we formalize a key property of efficient gathering protocols and use it to define λ-contracting protocols. Any such protocol gathers n robots in the d-dimensional space in 𝒪(Δ^2) synchronous rounds. Moreover, we prove a corresponding lower bound stating that any protocol in which robots move to target points inside of the local convex hulls of their neighborhoods – λ-contracting protocols have this property – requires Ω(Δ^2) rounds to gather all robots. Among others, we prove that the d-dimensional generalization of the GtC-protocol is λ-contracting. Remarkably, our improved and generalized runtime bound is independent of n and d. The independence of d answers an open research question. We also introduce an approach to make any λ-contracting protocol collisionfree to solve near-gathering. The resulting protocols maintain the runtime of Θ (Δ^2) and work even in the semi-synchronous model.Jannik Castenow, Jonas Harbig, Daniel Jung, Peter Kling, Till Knollmann, Friedhelm Meyer auf der Heidework_mwvpmikhsjd2tiii6fbygstcbuFri, 09 Sep 2022 00:00:00 GMTSymmetrization in the Calculation Pipeline of Gauss Function-Based Modeling of Hydrophobicity in Protein Structures
https://scholar.archive.org/work/3dkrz2ii35f2laihdudeij7e5m
In this paper, we show, discuss, and compare the effects of symmetrization in two calculation subroutines of the Fuzzy Oil Drop model, a coarse-grained model of density of hydrophobicity in proteins. In the FOD model, an input structure is enclosed in an axis-aligned ellipsoid called a drop. Two profiles of hydrophobicity are then calculated for its residues: theoretical (based on the 3D Gauss function) and observed (based on pairwise hydrophobic interactions). Condition of the hydrophobic core is revealed by comparing those profiles through relative entropy, while analysis of their local differences allows, in particular, determination of the starting location for the search for protein–protein and protein–ligand interaction areas. Here, we improve the baseline workflow of the FOD model by introducing symmetry to the hydrophobicity profile comparison and ellipsoid bounding procedures. In the first modification (FOD–JS), Kullback–Leibler divergence is enhanced with its Jensen–Shannon variant. In the second modification (FOD-PCA), the molecule is optimally aligned with the axes of the coordinate system via principal component analysis, and the size of its drop is determined by the standard deviation of all its effective atoms, making it less susceptible to structural outliers. Tests on several molecules with various shapes and functions confirm that the proposed modifications improve the accuracy, robustness, speed, and usability of Gauss function-based modeling of the density of hydrophobicity in protein structures.Mateusz Banachwork_3dkrz2ii35f2laihdudeij7e5mThu, 08 Sep 2022 00:00:00 GMTComputable Centering Methods for Spiraling Algorithms and their Duals, with Motivations from the theory of Lyapunov Functions
https://scholar.archive.org/work/2mzoyibqkfahjeunzuyxqc5l6m
For many problems, some of which are reviewed in the paper, popular algorithms like Douglas--Rachford (DR), ADMM, and FISTA produce approximating sequences that show signs of spiraling toward the solution. We present a meta-algorithm that exploits such dynamics to potentially enhance performance. The strategy of this meta-algorithm is to iteratively build and minimize surrogates for the Lyapunov function that captures those dynamics. As a first motivating application, we show that for prototypical feasibility problems the circumcentered-reflection method (CRM), subgradient projections, and Newton--Raphson are all describable as gradient-based methods for minimizing Lyapunov functions constructed for DR operators, with the former returning the minimizers of spherical surrogates for the Lyapunov function. As a second motivating application, we introduce a new method that shares these properties but with the added advantages that it: 1) does not rely on subproblems (e.g. reflections) and so may be applied for any operator whose iterates have the spiraling property; 2) provably has the aforementioned Lyapunov properties with few structural assumptions and so is generically suitable for primal/dual implementation; and 3) maps spaces of reduced dimension into themselves whenever the original operator does. This makes possible the first primal/dual implementation of a method that seeks the center of spiraling iterates. We describe this method, and provide a computed example (basis pursuit).Scott B. Lindstromwork_2mzoyibqkfahjeunzuyxqc5l6mThu, 08 Sep 2022 00:00:00 GMTUniversality for two-dimensional critical cellular automata
https://scholar.archive.org/work/ro3wmpmdwzbdljos6um67mdami
We study the class of monotone, two-state, deterministic cellular automata, in which sites are activated (or 'infected') by certain configurations of nearby infected sites. These models have close connections to statistical physics, and several specific examples have been extensively studied in recent years by both mathematicians and physicists. This general setting was first studied only recently, however, by Bollobás, Smith and Uzzell, who showed that the family of all such 'bootstrap percolation' models on ℤ^2 can be naturally partitioned into three classes, which they termed subcritical, critical and supercritical. In this paper we determine the order of the threshold for percolation (complete occupation) for every critical bootstrap percolation model in two dimensions. This 'universality' theorem includes as special cases results of Aizenman and Lebowitz, Gravner and Griffeath, Mountford, and van Enter and Hulshof, significantly strengthens bounds of Bollobás, Smith and Uzzell, and complements recent work of Balister, Bollobás, Przykucki and Smith on subcritical models.Béla Bollobás, Hugo Duminil-Copin, Robert Morris, Paul Smithwork_ro3wmpmdwzbdljos6um67mdamiThu, 08 Sep 2022 00:00:00 GMTDetection and Mapping of Specular Surfaces Using Multibounce Lidar Returns
https://scholar.archive.org/work/libngbdgdrgwno4rrocgqstgra
We propose methods that use specular, multibounce lidar returns to detect and map specular surfaces that might be invisible to conventional lidar systems that rely on direct, single-scatter returns. We derive expressions that relate the time- and angle-of-arrival of these multibounce returns to scattering points on the specular surface, and then use these expressions to formulate techniques for retrieving specular surface geometry when the scene is scanned by a single beam or illuminated with a multi-beam flash. We also consider the special case of transparent specular surfaces, for which surface reflections can be mixed together with light that scatters off of objects lying behind the surface.Connor Henley, Siddharth Somasundaram, Joseph Hollmann, Ramesh Raskarwork_libngbdgdrgwno4rrocgqstgraWed, 07 Sep 2022 00:00:00 GMTEstimating the Effects of Syrian Civil War
https://scholar.archive.org/work/ytagsraaejcy5oobmx7u2cnqie
We examine the effect of civil war in Syria on economic growth, human development and institutional quality. Building on the synthetic control method, we estimate the missing counterfactual scenario in the hypothetical absence of the armed conflict that led to unprecedented humanitarian crisis and population displacement in modern history. By matching Syrian growth and development trajectories with the characteristics of the donor pool of 66 countries with no armed internal conflict in the period 1996-2021, we estimate a series of growth and development gaps attributed to civil war. Syrian civil war appears to have had a temporary negative effect on the trajectory of economic growth that almost disappeared before the onset of COVID19 pandemic. By contrast, the civil war led to unprecedented losses in human development, rising infant mortality and rampantly deteriorating institutional quality. Down to the present day, each year of the conflict led to 5,700 additional under-five child deaths with permanently derailed negative effect on longevity. The civil war led to unprecedent and permanent deterioration in institutional quality indicated by pervasive weakening of the rule of law and deleterious impacts on government effectiveness, civil liberties and widespread escalation of corruption. The estimated effects survive a battery of placebo checks.Aleksandar Keseljevic, Rok Sprukwork_ytagsraaejcy5oobmx7u2cnqieWed, 07 Sep 2022 00:00:00 GMTTesting quantum theory with generalized noncontextuality
https://scholar.archive.org/work/oyhua622fng5flmomft3ljb7rm
It is a fundamental prediction of quantum theory that states of physical systems are described by complex vectors or density operators on a Hilbert space. However, many experiments admit effective descriptions in terms of other state spaces, such as classical probability distributions or quantum systems with superselection rules. Here, we ask which probabilistic theories could reasonably be found as effective descriptions of physical systems if nature is fundamentally quantum. To this end, we employ a generalized version of noncontextuality: processes that are statistically indistinguishable in an effective theory should not require explanation by multiple distinguishable processes in a more fundamental theory. We formulate this principle in terms of embeddings and simulations of one probabilistic theory by another, show how this concept subsumes standard notions of contextuality, and prove a multitude of fundamental results on the exact and approximate embedding of theories (in particular into quantum theory). We show how results on Bell inequalities can be used for the robust certification of generalized contextuality. From this, we propose an experimental test of quantum theory by probing single physical systems without assuming access to a tomographically complete set of procedures, arguably avoiding a significant loophole of earlier approaches.Markus P. Mueller, Andrew J. P. Garnerwork_oyhua622fng5flmomft3ljb7rmWed, 07 Sep 2022 00:00:00 GMTManifold Free Riemannian Optimization
https://scholar.archive.org/work/sy2ybuztfvbobidkesk7ey6j2e
Riemannian optimization is a principled framework for solving optimization problems where the desired optimum is constrained to a smooth manifold ℳ. Algorithms designed in this framework usually require some geometrical description of the manifold, which typically includes tangent spaces, retractions, and gradients of the cost function. However, in many cases, only a subset (or none at all) of these elements can be accessed due to lack of information or intractability. In this paper, we propose a novel approach that can perform approximate Riemannian optimization in such cases, where the constraining manifold is a submanifold of ^D. At the bare minimum, our method requires only a noiseless sample set of the cost function (_i, y_i)∈ℳ×ℝ and the intrinsic dimension of the manifold ℳ. Using the samples, and utilizing the Manifold-MLS framework (Sober and Levin 2020), we construct approximations of the missing components entertaining provable guarantees and analyze their computational costs. In case some of the components are given analytically (e.g., if the cost function and its gradient are given explicitly, or if the tangent spaces can be computed), the algorithm can be easily adapted to use the accurate expressions instead of the approximations. We analyze the global convergence of Riemannian gradient-based methods using our approach, and we demonstrate empirically the strength of this method, together with a conjugate-gradients type method based upon similar principles.Boris Shustin, Haim Avron, Barak Soberwork_sy2ybuztfvbobidkesk7ey6j2eWed, 07 Sep 2022 00:00:00 GMTNeural Quantum States for Scientific Computing: Applications to Computational Chemistry and Finance
https://scholar.archive.org/work/z3junf2h2jdtvcdanbbffnwj4y
The variational quantum Monte Carlo (VQMC) method has received significant attention because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems, by representing the exponentially complex quantum states variationally with machine learning models. We develop novel training strategies to improve the scalability of VQMC, and build parallelization frameworks for solving large-scale problems. The application of our method is extended to quantum chemistry and financial derivative pricing. For quantum chemistry, we build a pre-processing pipeline serving as an interface connecting molecular information and VQMC, and achieve remarkable performance in comparison with the classical approximate methods. On the other hand, we present a simple generalization of VQMC applicable to arbitrary linear PDEs, showcasing the technique in the Black-Scholes equation for pricing European contingent claims dependent on many underlying assets. We also introduce meta-learning and multi-fidelity active learning as exotic components to VQMC, which, under some reasonable assumptions on the problem formulation, can further improve the convergence and the sampling efficiency of our method.Tianchen Zhao, University, Mywork_z3junf2h2jdtvcdanbbffnwj4yTue, 06 Sep 2022 00:00:00 GMT