We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction. With the proposed framework, the target function is approximated by a mixture of experts model on a low-dimensional manifold, where each cluster is associated with a local fixed-degree polynomial. We present a training strategy that leverages the expectation maximization (EM) algorithm. During the training, we alternate between (i) applying gradient descent to update the DNN coefficients; and (ii) using closed-form formulae derived from the EM algorithm to update the mixture of experts model parameters. Under the probabilistic formulation, step (ii) admits the form of embarrassingly parallelizable weighted least-squares solves. The PPOU-Nets consistently outperform the baseline fully-connected neural networks of comparable sizes in numerical experiments of various data dimensions. We also explore the proposed model in applications of quantum computing, where the PPOU-Nets act as surrogate models for cost landscapes associated with variational quantum circuits.
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Networking：IFIP International Conferences on Networking。
Explanation：國際網絡會議。
Publisher：IFIP。
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To understand the ability and limitations of convolutional neural networks to generate time series that mimic complex temporal signals, we trained a generative adversarial network consisting of deep convolutional networks to generate chaotic time series and used nonlinear time series analysis to evaluate the generated time series. A numerical measure of determinism and the Lyapunov exponent, a measure of trajectory instability, showed that the generated time series well reproduce the chaotic properties of the original time series. However, error distribution analyses showed that large errors appeared at a low but non-negligible rate. Such errors would not be expected if the distribution were assumed to be exponential.
In the future, it is anticipated that software-defined networking (SDN) will become the preferred platform for deploying diverse networks. Compared to traditional networks, SDN separates the control and data planes for efficient domain-wide traffic routing and management. The controllers in the control plane are responsible for programming data plane forwarding devices, while the top layer, the application plane, enforces policies and programs the network. The different levels of the SDN use interfaces for communication. However, SDN faces challenges with traffic distribution, such as load imbalance, which can negatively affect the network performance. Consequently, developers have developed various SDN load-balancing solutions to enhance SDN effectiveness. In addition, researchers are considering the potential of implementing some artificial intelligence (AI) approaches into SDN to improve network resource usage and overall performance due to the fast growth of the AI field. This survey focuses on the following: Firstly, analyzing the SDN architecture and investigating the problem of load balancing in SDN. Secondly, categorizing AI-based load balancing methods and thoroughly assessing these mechanisms from various perspectives, such as the algorithm/technique employed, the tackled problem, and their strengths and weaknesses. Thirdly, summarizing the metrics utilized to measure the effectiveness of these techniques. Finally, identifying the trends and challenges of AI-based load balancing for future research.
In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the domain decomposition approach, we derive an optimal control problem, for which we present the convergence analysis. The snapshots for the high-fidelity model are obtained with the Finite Element discretisation, and the model order reduction is then proposed both in terms of time and physical parameters, with a standard POD-Galerkin projection. We test the proposed methodology on two fluid dynamics benchmarks: the non-stationary backward-facing step and lid-driven cavity flow. Finally, also in view of future works, we compare the intrusive POD--Galerkin approach with a non--intrusive approach based on Neural Networks.
An established normative approach for understanding the algorithmic basis of neural computation is to derive online algorithms from principled computational objectives and evaluate their compatibility with anatomical and physiological observations. Similarity matching objectives have served as successful starting points for deriving online algorithms that map onto neural networks (NNs) with point neurons and Hebbian/anti-Hebbian plasticity. These NN models account for many anatomical and physiological observations; however, the objectives have limited computational power and the derived NNs do not explain multi-compartmental neuronal structures and non-Hebbian forms of plasticity that are prevalent throughout the brain. In this article, we unify and generalize recent extensions of the similarity matching approach to address more complex objectives, including a large class of unsupervised and self-supervised learning tasks that can be formulated as symmetric generalized eigenvalue problems or nonnegative matrix factorization problems. Interestingly, the online algorithms derived from these objectives naturally map onto NNs with multi-compartmental neurons and local, non-Hebbian learning rules. Therefore, this unified extension of the similarity matching approach provides a normative framework that facilitates understanding multi-compartmental neuronal structures and non-Hebbian plasticity found throughout the brain.
We develop new matching estimators for estimating causal quantile exposure-response functions and quantile exposure effects with continuous treatments. We provide identification results for the parameters of interest and establish the asymptotic properties of the derived estimators. We introduce a two-step estimation procedure. In the first step, we construct a matched data set via generalized propensity score matching, adjusting for measured confounding. In the second step, we fit a kernel quantile regression to the matched set. We also derive a consistent estimator of the variance of the matching estimators. Using simulation studies, we compare the introduced approach with existing alternatives in various settings. We apply the proposed method to Medicare claims data for the period 2012-2014, and we estimate the causal effect of exposure to PM$_{2.5}$ on the length of hospital stay for each zip code of the contiguous United States.
We consider the degree-Rips construction from topological data analysis, which provides a density-sensitive, multiparameter hierarchical clustering algorithm. We analyze its stability to perturbations of the input data using the correspondence-interleaving distance, a metric for hierarchical clusterings that we introduce. Taking certain one-parameter slices of degree-Rips recovers well-known methods for density-based clustering, but we show that these methods are unstable. However, we prove that degree-Rips, as a multiparameter object, is stable, and we propose an alternative approach for taking slices of degree-Rips, which yields a one-parameter hierarchical clustering algorithm with better stability properties. We prove that this algorithm is consistent, using the correspondence-interleaving distance. We provide an algorithm for extracting a single clustering from one-parameter hierarchical clusterings, which is stable with respect to the correspondence-interleaving distance. And, we integrate these methods into a pipeline for density-based clustering, which we call Persistable. Adapting tools from multiparameter persistent homology, we propose visualization tools that guide the selection of all parameters of the pipeline. We demonstrate Persistable on benchmark datasets, showing that it identifies multi-scale cluster structure in data.
Training robust speaker verification systems without speaker labels has long been a challenging task. Previous studies observed a large performance gap between self-supervised and fully supervised methods. In this paper, we apply a non-contrastive self-supervised learning framework called DIstillation with NO labels (DINO) and propose two regularization terms applied to embeddings in DINO. One regularization term guarantees the diversity of the embeddings, while the other regularization term decorrelates the variables of each embedding. The effectiveness of various data augmentation techniques are explored, on both time and frequency domain. A range of experiments conducted on the VoxCeleb datasets demonstrate the superiority of the regularized DINO framework in speaker verification. Our method achieves the state-of-the-art speaker verification performance under a single-stage self-supervised setting on VoxCeleb. Code has been made publicly available at //github.com/alibaba-damo-academy/3D-Speaker.
Sequential fundraising in two sided online platforms enable peer to peer lending by sequentially bringing potential contributors, each of whose decisions impact other contributors in the market. However, understanding the dynamics of sequential contributions in online platforms for peer lending has been an open ended research question. The centralized investment mechanism in these platforms makes it difficult to understand the implicit competition that borrowers face from a single lender at any point in time. Matching markets are a model of pairing agents where the preferences of agents from both sides in terms of their preferred pairing for transactions can allow to decentralize the market. We study investment designs in two sided platforms using matching markets when the investors or lenders also face restrictions on the investments based on borrower preferences. This situation creates an implicit competition among the lenders in addition to the existing borrower competition, especially when the lenders are uncertain about their standing in the market and thereby the probability of their investments being accepted or the borrower loan requests for projects reaching the reserve price. We devise a technique based on sequential decision making that allows the lenders to adjust their choices based on the dynamics of uncertainty from competition over time. We simulate two sided market matchings in a sequential decision framework and show the dynamics of the lender regret amassed compared to the optimal borrower-lender matching and find that the lender regret depends on the initial preferences set by the lenders which could affect their learning over decision making steps.
We present Surjective Sequential Neural Likelihood (SSNL) estimation, a novel method for simulation-based inference in models where the evaluation of the likelihood function is not tractable and only a simulator that can generate synthetic data is available. SSNL fits a dimensionality-reducing surjective normalizing flow model and uses it as a surrogate likelihood function which allows for conventional Bayesian inference using either Markov chain Monte Carlo methods or variational inference. By embedding the data in a low-dimensional space, SSNL solves several issues previous likelihood-based methods had when applied to high-dimensional data sets that, for instance, contain non-informative data dimensions or lie along a lower-dimensional manifold. We evaluate SSNL on a wide variety of experiments and show that it generally outperforms contemporary methods used in simulation-based inference, for instance, on a challenging real-world example from astrophysics which models the magnetic field strength of the sun using a solar dynamo model.
In this paper, we develop a unified regression approach to model unconditional quantiles, M-quantiles and expectiles of multivariate dependent variables exploiting the multidimensional Huber's function. To assess the impact of changes in the covariates across the entire unconditional distribution of the responses, we extend the work of Firpo et al. (2009) by running a mean regression of the recentered influence function on the explanatory variables. We discuss the estimation procedure and establish the asymptotic properties of the derived estimators. A data-driven procedure is also presented to select the tuning constant of the Huber's function. The validity of the proposed methodology is explored with simulation studies and through an application using the Survey of Household Income and Wealth 2016 conducted by the Bank of Italy.
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