An overarching goal in machine learning is to build a generalizable model with few samples. To this end, overparameterization has been the subject of immense interest to explain the generalization ability of deep nets even when the size of the dataset is smaller than that of the model. While the prior literature focuses on the classical supervised setting, this paper aims to demystify overparameterization for meta-learning. Here we have a sequence of linear-regression tasks and we ask: (1) Given earlier tasks, what is the optimal linear representation of features for a new downstream task? and (2) How many samples do we need to build this representation? This work shows that surprisingly, overparameterization arises as a natural answer to these fundamental meta-learning questions. Specifically, for (1), we first show that learning the optimal representation coincides with the problem of designing a task-aware regularization to promote inductive bias. We leverage this inductive bias to explain how the downstream task actually benefits from overparameterization, in contrast to prior works on few-shot learning. For (2), we develop a theory to explain how feature covariance can implicitly help reduce the sample complexity well below the degrees of freedom and lead to small estimation error. We then integrate these findings to obtain an overall performance guarantee for our meta-learning algorithm. Numerical experiments on real and synthetic data verify our insights on overparameterized meta-learning.

Bayesian methods to solve imaging inverse problems usually combine an explicit data likelihood function with a prior distribution that explicitly models expected properties of the solution. Many kinds of priors have been explored in the literature, from simple ones expressing local properties to more involved ones exploiting image redundancy at a non-local scale. In a departure from explicit modelling, several recent works have proposed and studied the use of implicit priors defined by an image denoising algorithm. This approach, commonly known as Plug & Play (PnP) regularisation, can deliver remarkably accurate results, particularly when combined with state-of-the-art denoisers based on convolutional neural networks. However, the theoretical analysis of PnP Bayesian models and algorithms is difficult and works on the topic often rely on unrealistic assumptions on the properties of the image denoiser. This papers studies maximum-a-posteriori (MAP) estimation for Bayesian models with PnP priors. We first consider questions related to existence, stability and well-posedness, and then present a convergence proof for MAP computation by PnP stochastic gradient descent (PnP-SGD) under realistic assumptions on the denoiser used. We report a range of imaging experiments demonstrating PnP-SGD as well as comparisons with other PnP schemes.

Latest library version: 1.0.1 (see Release notes for more info) The GDLibrary is a pure-Matlab library of a collection of unconstrained optimization algorithms. This solves an unconstrained minimization problem of the form, min f(x). Note that the SGDLibrary internally contains this GDLibrary. Run run_me_first for path configurations. Now, just execute demo for demonstration of this package.

As a teacher of Data Science (Data Science for Internet of Things course at the University of Oxford), I am always fascinated in cross connection between concepts. To recap, Logistic regression is a binary classification method. It can be modelled as a function that can take in any number of inputs and constrain the output to be between 0 and 1. This means, we can think of Logistic Regression as a one-layer neural network. For a binary output, if the true label is y (y 0 or y 1) and y_hat is the predicted output – then y_hat represents the probability that y 1 – given inputs w and x. Therefore, the probability that y 0 given inputs w and x is (1 – y_hat), as shown below.

As 2021 draws to a close, I'm energized by all the amazing work completed by many prominent research groups extending the state of machine learning in a variety of important directions. In this article, I'll keep you up to date with my top picks of machine learning research papers for the last half of 2021 that I found particularly compelling and useful. Through my effort to stay current with the field's research advancement, I found the directions represented in these machine learning research papers to be very promising. I hope you enjoy my selections as much as I have. Most algorithms in classical and contemporary machine learning focus on correlation-based dependence between features to drive performance.

The mortality rate for pedestrians using wheelchairs was 36% higher than the overall population pedestrian mortality rate. However, there is no data to clarify the pedestrians' categories in both fatal and nonfatal accidents, since police reports often do not keep a record of whether a victim was using a wheelchair or has a disability. Currently, real-time detection of vulnerable road users using advanced traffic sensors installed at the infrastructure side has a great potential to significantly improve traffic safety at the intersection. In this research, we develop a systematic framework with a combination of machine learning and deep learning models to distinguish disabled people from normal walk pedestrians and predict the time needed to reach the next side of the intersection. The proposed framework shows high performance both at vulnerable user classification and arrival time prediction accuracy.

When minimising the empirical risk, the generalisation of the learnt function still depends on the performance on the training data, the Vapnik-Chervonenkis(VC)- dimension of the function and the number of training examples. Neural networks have a large number of parameters, which correlates with their VC-dimension that is typically large but not infinite, and typically a large number of training instances are needed to effectively train them. In this work, we explore how to optimize feature mappings using neural network with the intention to reduce the effective VC-dimension of the hyperplane found in the space generatedby the mapping. An interpretationofthe resultsofthis study isthat it ispossible to define a loss that controls the VC-dimension of the separating hyperplane. We evaluate this approach and observe that the performance when using this method improves when the size of the training set is small.

Patients are often encouraged to make use of wearable devices for remote collection and monitoring of health data. This adoption of wearables results in a significant increase in the volume of data collected and transmitted. The battery life of the devices is then quickly diminished due to the high processing requirements of the devices. Given the importance attached to medical data, it is imperative that all transmitted data adhere to strict integrity and availability requirements. Reducing the volume of healthcare data for network transmission may improve sensor battery life without compromising accuracy. There is a trade-off between efficiency and accuracy which can be controlled by adjusting the sampling and transmission rates. This paper demonstrates that machine learning can be used to analyse complex health data metrics such as the accuracy and efficiency of data transmission to overcome the trade-off problem. The study uses time series nonlinear autoregressive neural network algorithms to enhance both data metrics by taking fewer samples to transmit. The algorithms were tested with a standard heart rate dataset to compare their accuracy and efficiency. The result showed that the Levenbery-Marquardt algorithm was the best performer with an efficiency of 3.33 and accuracy of 79.17%, which is similar to other algorithms accuracy but demonstrates improved efficiency. This proves that machine learning can improve without sacrificing a metric over the other compared to the existing methods with high efficiency.

Probabilistic models often use neural networks to control their predictive uncertainty. However, when making out-of-distribution (OOD)} predictions, the often-uncontrollable extrapolation properties of neural networks yield poor uncertainty predictions. Such models then don't know what they don't know, which directly limits their robustness w.r.t unexpected inputs. To counter this, we propose to explicitly train the uncertainty predictor where we are not given data to make it reliable. As one cannot train without data, we provide mechanisms for generating pseudo-inputs in informative low-density regions of the input space, and show how to leverage these in a practical Bayesian framework that casts a prior distribution over the model uncertainty. With a holistic evaluation, we demonstrate that this yields robust and interpretable predictions of uncertainty while retaining state-of-the-art performance on diverse tasks such as regression and generative modelling

We study the subject of universal online learning with non-i.i.d. processes for bounded losses. The notion of an universally consistent learning was defined by Hanneke in an effort to study learning theory under minimal assumptions, where the objective is to obtain low long-run average loss for any target function. We are interested in characterizing processes for which learning is possible and whether there exist learning rules guaranteed to be universally consistent given the only assumption that such learning is possible. The case of unbounded losses is very restrictive, since the learnable processes almost surely visit a finite number of points and as a result, simple memorization is optimistically universal. We focus on the bounded setting and give a complete characterization of the processes admitting strong and weak universal learning. We further show that k-nearest neighbor algorithm (kNN) is not optimistically universal and present a novel variant of 1NN which is optimistically universal for general input and value spaces in both strong and weak setting. This closes all COLT 2021 open problems posed by Hanneke on universal online learning.