Langevin Quasi-Monte Carlo

Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density $\pi(\theta)\propto \exp(-U(\theta))$, LMC iteratively generates the next sample by taking a step in the gradient direction $\nabla U$ with added Gaussian perturbations. Expectations w.r.t. the target distribution $\pi$ are estimated by averaging over LMC samples. In ordinary Monte Carlo, it is well known that the estimation error can be substantially reduced by replacing independent random samples by quasi-random samples like low-discrepancy sequences. In this work, we show that the estimation error of LMC can also be reduced by using quasi-random samples. Specifically, we propose to use completely uniformly distributed (CUD) sequences with certain low-discrepancy property to generate the Gaussian perturbations. Under smoothness and convexity conditions, we prove that LMC with a low-discrepancy CUD sequence achieves smaller error than standard LMC. The theoretical analysis is supported by compelling numerical experiments, which demonstrate the effectiveness of our approach

Conditional Quasi-Monte Carlo with Constrained Active Subspaces

Conditional Monte Carlo or pre-integration is a useful tool for reducing variance and improving regularity of integrands when applying Monte Carlo and quasi-Monte Carlo (QMC) methods. To choose the variable to pre-integrate with, one need to consider both the variable importance and the tractability of the conditional expectation. For integrals over a Gaussian distribution, one can pre-integrate over any linear combination of variables. Liu and Owen (2022) propose to choose the linear combination based on an active subspace decomposition of the integrand. However, pre-integrating over such selected direction might be intractable. In this work, we address this issue by finding the active subspaces subject to the constraints such that pre-integration can be easily carried out. The proposed method is applied to some examples in derivative pricing under stochastic volatility models and is shown to outperform previous methods

An Exact Sampler for Inference after Polyhedral Model Selection

Inference after model selection presents computational challenges when dealing with intractable conditional distributions. Markov chain Monte Carlo (MCMC) is a common method for sampling from these distributions, but its slow convergence often limits its practicality. In this work, we introduce a method tailored for selective inference in cases where the selection event can be characterized by a polyhedron. The method transforms the variables constrained by a polyhedron into variables within a unit cube, allowing for efficient sampling using conventional numerical integration techniques. Compared to MCMC, the proposed sampling method is highly accurate and equipped with an error estimate. Additionally, we introduce an approach to use a single batch of samples for hypothesis testing and confidence interval construction across multiple parameters, reducing the need for repetitive sampling. Furthermore, our method facilitates fast and precise computation of the maximum likelihood estimator based on the selection-adjusted likelihood, enhancing the reliability of MLE-based inference. Numerical results demonstrate the superior performance of the proposed method compared to alternative approaches for selective inference

The digitalisation of everything: How the US economy is going digital at hyper speed

Since 2002, the share of jobs requiring extensive and mid-level digital skills has surged from 45 to 71 per cent of the total, write Mark Muro and Sifan Li

Selective Inference with Distributed Data

As datasets grow larger, they are often distributed across multiple machines that compute in parallel and communicate with a central machine through short messages. In this paper, we focus on sparse regression and propose a new procedure for conducting selective inference with distributed data. Although many distributed procedures exist for point estimation in the sparse setting, few options are available for estimating uncertainties or conducting hypothesis tests based on the estimated sparsity. We solve a generalized linear regression on each machine, which then communicates a selected set of predictors to the central machine. The central machine uses these selected predictors to form a generalized linear model (GLM). To conduct inference in the selected GLM, our proposed procedure bases approximately-valid selective inference on an asymptotic likelihood. The proposal seeks only aggregated information, in relatively few dimensions, from each machine which is merged at the central machine for selective inference. By reusing low-dimensional summary statistics from local machines, our procedure achieves higher power while keeping the communication cost low. This method is also applicable as a solution to the notorious p-value lottery problem that arises when model selection is repeated on random splits of data

Cooperative Cell-Free ISAC Networks: Joint BS Mode Selection and Beamforming Design

Owing to the promising ability of saving hardware cost and spectrum resources, integrated sensing and communication (ISAC) is regarded as a revolutionary technology for future sixth-generation (6G) networks. The mono-static ISAC systems considered in most of existing works can only achieve limited sensing performance due to the single observation angle and easily blocked transmission links, which motivates researchers to investigate cooperative ISAC networks. In order to further improve the degrees of freedom (DoFs) of cooperative ISAC networks, the transmitter-receiver selection, i.e., base station (BS) mode selection problem, is meaningful to be studied. However, to our best knowledge, this crucial problem has not been extensively studied in existing works. In this paper, we consider the joint BS mode selection, transmit beamforming, and receive filter design for cooperative cell-free ISAC networks, where multi-BSs cooperatively serve communication users and detect targets. We aim to maximize the sum of sensing signal-to-interference-plus-noise ratio (SINR) under the communication SINR requirements, total power budget, and constraints on the numbers of transmit/receive BSs. An efficient joint beamforming design algorithm and three different heuristic BS mode selection methods are proposed to solve this non-convex NP-hard problem. Simulation results demonstrates the advantages of cooperative ISAC networks, the importance of BS mode selection, and the effectiveness of our proposed algorithms

New Identities of China’s Private Art Museum within the Scope of Global Art World

Màster Oficial en Gestió Cultural, Universitat de Barcelona. Facultat d’Economia i Empresa , curs: 2018-2019, Tutor: Dr. Francesc Xavier RoigéBased on a worldview, the core issue of cultural globalization is pacing toward the contemporary art world. Within the triangular circuit among contemporary art museums, global art markets and the plurality of identity from a world scape, the role play of contemporary art museum pushes itself on the crest of a wave. From the first shaping of a “white box” to today’s spectacular architecture, the accelerated speed of its “reproducible” construction gives today’s contemporary art museum an opportunity to mapping a global journey under the umbrella of “global art” (Völckers & Farenholtz, 2013). For all we know, such sense of “global” implicates the threats of singularity and homogenization, which are intensified in partial non-western counties and regions. That is to say, during the postwar time, the global (contemporary) art indicates the tremendous expansion of its regional and world circulation targeting on these nonwestern counties and regions (Mosquera, 2001). To interplant these “mass-produced artistic goods” reasonably, one of the crucial role play of the new museums here is to actualize as an art market to ensure this circulation vitalized. Among these regional art markets, indisputably, China is one of the most characteristic cases. However, what is more intriguing that, the reason of the rising of contemporary art in China is initially due to a political issue. Impacted by the global art market this contemporary Chinese art shifted dramatically as the up-and-coming Chinese contemporary art (Wu Hung, 2008). Overnight, all the megapolis and Metropolis in China give the public a dazzling architecture show as the history once occurred in the Western repeats itself again. These vanity projects once again triggers a fierce debate about the function of a new museum and the orientation of a (contemporary) art museum in China. Meanwhile, continuously affected by globalization, the new models of contemporary art museum in western countries are also emerged in China, especially in the South China. Hereto, this final work aims to critically discuss the principal transformations of China’s (non-profit) private art museums which are actually characterized as private contemporary art museums under the world’s backgrounds of the issue about the mapping of global contemporary art museums. At the same time, this thesis also intends to observe the reactions and interactions between China’s private art museums and the influences of global museums’ brand identity by means of three in-depth-case analysis of China’s private art museums. Last but not least, through all the researches which are employed by the mixed methodology based on qualitative and quantitative approaches under the theoretical framework of new models of museums undertaken, this thesis would ultimately find out one of the feasible possibilities of new models for China’s private art museum’s future with a raised question of which is more significant between the issue of China’s private art museums will be and the issue about what China’s private art museums could include and present