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.
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Online active learning is a paradigm in machine learning that aims to select the most informative data points to label from a data stream. The problem of minimizing the cost associated with collecting labeled observations has gained a lot of attention in recent years, particularly in real-world applications where data is only available in an unlabeled form. Annotating each observation can be time-consuming and costly, making it difficult to obtain large amounts of labeled data. To overcome this issue, many active learning strategies have been proposed in the last decades, aiming to select the most informative observations for labeling in order to improve the performance of machine learning models. These approaches can be broadly divided into two categories: static pool-based and stream-based active learning. Pool-based active learning involves selecting a subset of observations from a closed pool of unlabeled data, and it has been the focus of many surveys and literature reviews. However, the growing availability of data streams has led to an increase in the number of approaches that focus on online active learning, which involves continuously selecting and labeling observations as they arrive in a stream. This work aims to provide an overview of the most recently proposed approaches for selecting the most informative observations from data streams in real time. We review the various techniques that have been proposed and discuss their strengths and limitations, as well as the challenges and opportunities that exist in this area of research.
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a Bayesian approach: Parameter and prediction uncertainties become easily available, facilitating rigorous statistical analysis. Furthermore, prior knowledge can be incorporated. However, so far, there have been no scalable techniques capable of combining both structural and parameter uncertainty. In this paper, we apply the concept of model uncertainty as a framework for structural learning in BNNs and hence make inference in the joint space of structures/models and parameters. Moreover, we suggest an adaptation of a scalable variational inference approach with reparametrization of marginal inclusion probabilities to incorporate the model space constraints. Experimental results on a range of benchmark datasets show that we obtain comparable accuracy results with the competing models, but based on methods that are much more sparse than ordinary BNNs.
IoT devices generating enormous data and state-of-the-art machine learning techniques together will revolutionize cyber-physical systems. In many diverse fields, from autonomous driving to augmented reality, distributed IoT devices compute specific target functions without simple forms like obstacle detection, object recognition, etc. Traditional cloud-based methods that focus on transferring data to a central location either for training or inference place enormous strain on network resources. To address this, we develop, to the best of our knowledge, the first machine learning framework for distributed functional compression over both the Gaussian Multiple Access Channel (GMAC) and orthogonal AWGN channels. Due to the Kolmogorov-Arnold representation theorem, our machine learning framework can, by design, compute any arbitrary function for the desired functional compression task in IoT. Importantly the raw sensory data are never transferred to a central node for training or inference, thus reducing communication. For these algorithms, we provide theoretical convergence guarantees and upper bounds on communication. Our simulations show that the learned encoders and decoders for functional compression perform significantly better than traditional approaches, are robust to channel condition changes and sensor outages. Compared to the cloud-based scenario, our algorithms reduce channel use by two orders of magnitude.
Theoretical studies on transfer learning or domain adaptation have so far focused on situations with a known hypothesis class or model; however in practice, some amount of model selection is usually involved, often appearing under the umbrella term of hyperparameter-tuning: for example, one may think of the problem of tuning for the right neural network architecture towards a target task, while leveraging data from a related source task. Now, in addition to the usual tradeoffs on approximation vs estimation errors involved in model selection, this problem brings in a new complexity term, namely, the transfer distance between source and target distributions, which is known to vary with the choice of hypothesis class. We present a first study of this problem, focusing on classification; in particular, the analysis reveals some remarkable phenomena: adaptive rates, i.e., those achievable with no distributional information, can be arbitrarily slower than oracle rates, i.e., when given knowledge on distances.
We study numerical integration over bounded regions in $\mathbb{R}^s, s\ge1$ with respect to some probability measure. We replace random sampling with quasi-Monte Carlo methods, where the underlying point set is derived from deterministic constructions that aim to fill the space more evenly than random points. Such quasi-Monte Carlo point sets are ordinarily designed for the uniform measure, and the theory only works for product measures when a coordinate-wise transformation is applied. Going beyond this setting, we first consider the case where the target density is a mixture distribution where each term in the mixture comes from a product distribution. Next we consider target densities which can be approximated with such mixture distributions. We require the approximation to be a sum of coordinate-wise products and the approximation to be positive everywhere (so that they can be re-scaled to probability density functions). We use tensor product hat function approximations for this purpose here, since a hat function approximation of a positive function is itself positive. We also study more complex algorithms, where we first approximate the target density with a general Gaussian mixture distribution and approximate the mixtures with an adaptive hat function approximation on rotated intervals. The Gaussian mixture approximation allows us to locate the essential parts of the target density, whereas the adaptive hat function approximation allows us to approximate the finer structure of the target density. We prove convergence rates for each of the integration techniques based on quasi-Monte Carlo sampling for integrands with bounded partial mixed derivatives. The employed algorithms are based on digital $(t,s)$-sequences over the finite field $\mathbb{F}_2$ and an inversion method. Numerical examples illustrate the performance of the algorithms for some target densities and integrands.
Deep learning (DL) has become a key component of modern software. In the "big model" era, the rich features of DL-based software substantially rely on powerful DL models, e.g., BERT, GPT-3, and the recently emerging GPT-4, which are trained on the powerful cloud with large datasets. Hence, training effective DL models has become a vital stage in the whole software lifecycle. When training deep learning models, especially those big models, developers need to parallelize and distribute the computation and memory resources amongst multiple devices in the training process, which is known as distributed deep learning training, or distributed training for short. However, the unique challenges that developers encounter in distributed training process have not been studied in the software engineering community. Given the increasingly heavy dependence of current DL-based software on distributed training, this paper aims to fill in the knowledge gap and presents the first comprehensive study on developers' issues in distributed training. To this end, we analyze 1,131 real-world developers' issues about using these frameworks reported on Stack Overflow and GitHub. We construct a fine-grained taxonomy consisting of 30 categories regarding the fault symptoms and summarize common fix patterns for different symptoms. Based on the results, we suggest actionable implications on research avenues that can potentially facilitate the distributed training to develop DL-based software, such as focusing on the frequent and common fix patterns when designing testing or debugging tools, developing efficient testing and debugging techniques for communication configuration along with the synthesis of network configuration analysis, designing new multi-device checkpoint-and-replay techniques to help reproduction, and designing serverless APIs for cloud platforms.
Federated machine learning is growing fast in academia and industries as a solution to solve data hungriness and privacy issues in machine learning. Being a widely distributed system, federated machine learning requires various system design thinking. To better design a federated machine learning system, researchers have introduced multiple patterns and tactics that cover various system design aspects. However, the multitude of patterns leaves the designers confused about when and which pattern to adopt. In this paper, we present a set of decision models for the selection of patterns for federated machine learning architecture design based on a systematic literature review on federated machine learning, to assist designers and architects who have limited knowledge of federated machine learning. Each decision model maps functional and non-functional requirements of federated machine learning systems to a set of patterns. We also clarify the drawbacks of the patterns. We evaluated the decision models by mapping the decision patterns to concrete federated machine learning architectures by big tech firms to assess the models' correctness and usefulness. The evaluation results indicate that the proposed decision models are able to bring structure to the federated machine learning architecture design process and help explicitly articulate the design rationale.
Causal discovery and causal reasoning are classically treated as separate and consecutive tasks: one first infers the causal graph, and then uses it to estimate causal effects of interventions. However, such a two-stage approach is uneconomical, especially in terms of actively collected interventional data, since the causal query of interest may not require a fully-specified causal model. From a Bayesian perspective, it is also unnatural, since a causal query (e.g., the causal graph or some causal effect) can be viewed as a latent quantity subject to posterior inference -- other unobserved quantities that are not of direct interest (e.g., the full causal model) ought to be marginalized out in this process and contribute to our epistemic uncertainty. In this work, we propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning, which jointly infers a posterior over causal models and queries of interest. In our approach to ABCI, we focus on the class of causally-sufficient, nonlinear additive noise models, which we model using Gaussian processes. We sequentially design experiments that are maximally informative about our target causal query, collect the corresponding interventional data, and update our beliefs to choose the next experiment. Through simulations, we demonstrate that our approach is more data-efficient than several baselines that only focus on learning the full causal graph. This allows us to accurately learn downstream causal queries from fewer samples while providing well-calibrated uncertainty estimates for the quantities of interest.
In order to overcome the expressive limitations of graph neural networks (GNNs), we propose the first method that exploits vector flows over graphs to develop globally consistent directional and asymmetric aggregation functions. We show that our directional graph networks (DGNs) generalize convolutional neural networks (CNNs) when applied on a grid. Whereas recent theoretical works focus on understanding local neighbourhoods, local structures and local isomorphism with no global information flow, our novel theoretical framework allows directional convolutional kernels in any graph. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then we propose the use of the Laplacian eigenvectors as such vector field, and we show that the method generalizes CNNs on an n-dimensional grid, and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. Finally, we bring the power of CNN data augmentation to graphs by providing a means of doing reflection, rotation and distortion on the underlying directional field. We evaluate our method on different standard benchmarks and see a relative error reduction of 8\% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset. An important outcome of this work is that it enables to translate any physical or biological problems with intrinsic directional axes into a graph network formalism with an embedded directional field.
In recent years, mobile devices have gained increasingly development with stronger computation capability and larger storage. Some of the computation-intensive machine learning and deep learning tasks can now be run on mobile devices. To take advantage of the resources available on mobile devices and preserve users' privacy, the idea of mobile distributed machine learning is proposed. It uses local hardware resources and local data to solve machine learning sub-problems on mobile devices, and only uploads computation results instead of original data to contribute to the optimization of the global model. This architecture can not only relieve computation and storage burden on servers, but also protect the users' sensitive information. Another benefit is the bandwidth reduction, as various kinds of local data can now participate in the training process without being uploaded to the server. In this paper, we provide a comprehensive survey on recent studies of mobile distributed machine learning. We survey a number of widely-used mobile distributed machine learning methods. We also present an in-depth discussion on the challenges and future directions in this area. We believe that this survey can demonstrate a clear overview of mobile distributed machine learning and provide guidelines on applying mobile distributed machine learning to real applications.
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