Mutual Information (MI) plays an important role in representation learning. However, MI is unfortunately intractable in continuous and high-dimensional settings. Recent advances establish tractable and scalable MI estimators to discover useful representation. However, most of the existing methods are not capable of providing an accurate estimation of MI with low-variance when the MI is large. We argue that directly estimating the gradients of MI is more appealing for representation learning than estimating MI in itself. To this end, we propose the Mutual Information Gradient Estimator (MIGE) for representation learning based on the score estimation of implicit distributions. MIGE exhibits a tight and smooth gradient estimation of MI in the high-dimensional and large-MI settings. We expand the applications of MIGE in both unsupervised learning of deep representations based on InfoMax and the Information Bottleneck method. Experimental results have indicated significant performance improvement in learning useful representation.

Federated learning has received great attention for its capability to train a large-scale model in a decentralized manner without needing to access user data directly. It helps protect the users' private data from centralized collecting. Unlike distributed machine learning, federated learning aims to tackle non-IID data from heterogeneous sources in various real-world applications, such as those on smartphones. Existing federated learning approaches usually adopt a single global model to capture the shared knowledge of all users by aggregating their gradients, regardless of the discrepancy between their data distributions. However, due to the diverse nature of user behaviors, assigning users' gradients to different global models (i.e., centers) can better capture the heterogeneity of data distributions across users. Our paper proposes a novel multi-center aggregation mechanism for federated learning, which learns multiple global models from the non-IID user data and simultaneously derives the optimal matching between users and centers. We formulate the problem as a joint optimization that can be efficiently solved by a stochastic expectation maximization (EM) algorithm. Our experimental results on benchmark datasets show that our method outperforms several popular federated learning methods.

We present a generic and flexible Reinforcement Learning (RL) based meta-learning framework for the problem of few-shot learning. During training, it learns the best optimization algorithm to produce a learner (ranker/classifier, etc) by exploiting stable patterns in loss surfaces. Our method implicitly estimates the gradients of a scaled loss function while retaining the general properties intact for parameter updates. Besides providing improved performance on few-shot tasks, our framework could be easily extended to do network architecture search. We further propose a novel dual encoder, affinity-score based decoder topology that achieves additional improvements to performance. Experiments on an internal dataset, MQ2007, and AwA2 show our approach outperforms existing alternative approaches by 21%, 8%, and 4% respectively on accuracy and NDCG metrics. On Mini-ImageNet dataset our approach achieves comparable results with Prototypical Networks. Empirical evaluations demonstrate that our approach provides a unified and effective framework.

Deep neural models in recent years have been successful in almost every field, including extremely complex problem statements. However, these models are huge in size, with millions (and even billions) of parameters, thus demanding more heavy computation power and failing to be deployed on edge devices. Besides, the performance boost is highly dependent on redundant labeled data. To achieve faster speeds and to handle the problems caused by the lack of data, knowledge distillation (KD) has been proposed to transfer information learned from one model to another. KD is often characterized by the so-called `Student-Teacher' (S-T) learning framework and has been broadly applied in model compression and knowledge transfer. This paper is about KD and S-T learning, which are being actively studied in recent years. First, we aim to provide explanations of what KD is and how/why it works. Then, we provide a comprehensive survey on the recent progress of KD methods together with S-T frameworks typically for vision tasks. In general, we consider some fundamental questions that have been driving this research area and thoroughly generalize the research progress and technical details. Additionally, we systematically analyze the research status of KD in vision applications. Finally, we discuss the potentials and open challenges of existing methods and prospect the future directions of KD and S-T learning.

Machine learning algorithms are classified as two distinct groups: parametric and non-parametric. Herein, parametricness is related to pair of model complexity and the number of rows in the train set. We can classify algorithms as non-parametric when model becomes more complex if number of samples in the training set increases. Vice versa, a model would be parametric if model becomes stable when number of examples in the training set increases. If we increase the number of instances, then the decision tree that is going to be built becomes more complex.

In this module, we introduce the core idea of teaching a computer to learn concepts using data--without being explicitly programmed. The Course Wiki is under construction. Please visit the resources tab for the most complete and up-to-date information.

This article will explain you what Principal Component Analysis (PCA) is, why we need it and how we use it. I will try to make it as simple as possible while avoiding hard examples or words which can cause a headache. A moment of honesty: to fully understand this article, a basic understanding of some linear algebra and statistics is essential. Let's say we have 10 variables in our dataset and let's assume that 3 variables capture 90% of the dataset, and 7 variables capture 10% of the dataset. Let's say we want to visualize 10 variables.

Ill-posed linear inverse problems appear in many fields of imaging science and engineering, and are typically addressed by solving optimization problems, which are composed of fidelity and prior terms or constraints. Traditionally, the research has been focused on different prior models, while the least squares (LS) objective has been the common choice for the fidelity term. However, recently a few works have considered a back-projection (BP) based fidelity term as an alternative to the LS, and demonstrated excellent reconstruction results for popular inverse problems. These prior works have also empirically shown that using the BP term, rather than the LS term, requires fewer iterations of plain and accelerated proximal gradient algorithms. In the current paper, we examine the convergence rate of the BP objective for the projected gradient descent (PGD) algorithm and identify an inherent source for its faster convergence compared to the LS objective. Numerical experiments with both $\ell_1$-norm and GAN-based priors corroborate our theoretical results for PGD. We also draw the connection to the observed behavior for proximal methods.

This paper presents a novel accelerated exact k-means algorithm called the Ball k-means algorithm, which uses a ball to describe a cluster, focusing on reducing the point-centroid distance computation. The Ball k-means can accurately find the neighbor clusters for each cluster resulting distance computations only between a point and its neighbor clusters' centroids instead of all centroids. Moreover, each cluster can be divided into a stable area and an active area, and the later one can be further divided into annulus areas. The assigned cluster of the points in the stable area is not changed in the current iteration while the points in the annulus area will be adjusted within a few neighbor clusters in the current iteration. Also, there are no upper or lower bounds in the proposed Ball k-means. Furthermore, reducing centroid-centroid distance computation between iterations makes it efficient for large k clustering. The fast speed, no extra parameters and simple design of the Ball k-means make it an all-around replacement of the naive k-means algorithm.

This paper considers the decentralized optimization problem, which has applications in large scale machine learning, sensor networks, and control theory. We propose a novel algorithm that can achieve near optimal communication complexity, matching the known lower bound up to a logarithmic factor of the condition number of the problem. Our theoretical results give affirmative answers to the open problem on whether there exists an algorithm that can achieve a communication complexity (nearly) matching the lower bound depending on the global condition number instead of the local one. Moreover, the proposed algorithm achieves the optimal computation complexity matching the lower bound up to universal constants. Furthermore, to achieve a linear convergence rate, our algorithm \emph{doesn't} require the individual functions to be (strongly) convex. Our method relies on a novel combination of known techniques including Nesterov's accelerated gradient descent, multi-consensus and gradient-tracking. The analysis is new, and may be applied to other related problems. Empirical studies demonstrate the effectiveness of our method for machine learning applications.