Dirichlet Active Learning

This work introduces Dirichlet Active Learning (DiAL), a Bayesian-inspired approach to the design of active learning algorithms. Our framework models feature-conditional class probabilities as a Dirichlet random field and lends observational strength between similar features in order to calibrate the random field. This random field can then be utilized in learning tasks: in particular, we can use current estimates of mean and variance to conduct classification and active learning in the context where labeled data is scarce. We demonstrate the applicability of this model to low-label rate graph learning by constructing ``propagation operators'' based upon the graph Laplacian, and offer computational studies demonstrating the method's competitiveness with the state of the art. Finally, we provide rigorous guarantees regarding the ability of this approach to ensure both exploration and exploitation, expressed respectively in terms of cluster exploration and increased attention to decision boundaries.

Cluster-aware Semi-supervised Learning: Relational Knowledge Distillation Provably Learns Clustering

Despite the empirical success and practical significance of (relational) knowledge distillation that matches (the relations of) features between teacher and student models, the corresponding theoretical interpretations remain limited for various knowledge distillation paradigms. In this work, we take an initial step toward a theoretical understanding of relational knowledge distillation (RKD), with a focus on semi-supervised classification problems. We start by casting RKD as spectral clustering on a population-induced graph unveiled by a teacher model. Via a notion of clustering error that quantifies the discrepancy between the predicted and ground truth clusterings, we illustrate that RKD over the population provably leads to low clustering error. Moreover, we provide a sample complexity bound for RKD with limited unlabeled samples. For semi-supervised learning, we further demonstrate the label efficiency of RKD through a general framework of cluster-aware semi-supervised learning that assumes low clustering errors. Finally, by unifying data augmentation consistency regularization into this cluster-aware framework, we show that despite the common effect of learning accurate clusterings, RKD facilitates a "global" perspective through spectral clustering, whereas consistency regularization focuses on a "local" perspective via expansion.

Novel Batch Active Learning Approach and Its Application to Synthetic Aperture Radar Datasets

Active learning improves the performance of machine learning methods by judiciously selecting a limited number of unlabeled data points to query for labels, with the aim of maximally improving the underlying classifier's performance. Recent gains have been made using sequential active learning for synthetic aperture radar (SAR) data arXiv:2204.00005. In each iteration, sequential active learning selects a query set of size one while batch active learning selects a query set of multiple datapoints. While batch active learning methods exhibit greater efficiency, the challenge lies in maintaining model accuracy relative to sequential active learning methods. We developed a novel, two-part approach for batch active learning: Dijkstra's Annulus Core-Set (DAC) for core-set generation and LocalMax for batch sampling. The batch active learning process that combines DAC and LocalMax achieves nearly identical accuracy as sequential active learning but is more efficient, proportional to the batch size. As an application, a pipeline is built based on transfer learning feature embedding, graph learning, DAC, and LocalMax to classify the FUSAR-Ship and OpenSARShip datasets. Our pipeline outperforms the state-of-the-art CNN-based methods.

Graph-based Active Learning for Surface Water and Sediment Detection in Multispectral Images

We develop a graph active learning pipeline (GAP) to detect surface water and in-river sediment pixels in satellite images. The active learning approach is applied within the training process to optimally select specific pixels to generate a hand-labeled training set. Our method obtains higher accuracy with far fewer training pixels than both standard and deep learning models. According to our experiments, our GAP trained on a set of 3270 pixels reaches a better accuracy than the neural network method trained on 2.1 million pixels.

Poisson Reweighted Laplacian Uncertainty Sampling for Graph-based Active Learning

We show that uncertainty sampling is sufficient to achieve exploration versus exploitation in graph-based active learning, as long as the measure of uncertainty properly aligns with the underlying model and the model properly reflects uncertainty in unexplored regions. In particular, we use a recently developed algorithm, Poisson ReWeighted Laplace Learning (PWLL) for the classifier and we introduce an acquisition function designed to measure uncertainty in this graph-based classifier that identifies unexplored regions of the data. We introduce a diagonal perturbation in PWLL which produces exponential localization of solutions, and controls the exploration versus exploitation tradeoff in active learning. We use the well-posed continuum limit of PWLL to rigorously analyze our method, and present experimental results on a number of graph-based image classification problems.

Graph-based Active Learning for Semi-supervised Classification of SAR Data

We present a novel method for classification of Synthetic Aperture Radar (SAR) data by combining ideas from graph-based learning and neural network methods within an active learning framework. Graph-based methods in machine learning are based on a similarity graph constructed from the data. When the data consists of raw images composed of scenes, extraneous information can make the classification task more difficult. In recent years, neural network methods have been shown to provide a promising framework for extracting patterns from SAR images. These methods, however, require ample training data to avoid overfitting. At the same time, such training data are often unavailable for applications of interest, such as automatic target recognition (ATR) and SAR data. We use a Convolutional Neural Network Variational Autoencoder (CNNVAE) to embed SAR data into a feature space, and then construct a similarity graph from the embedded data and apply graph-based semi-supervised learning techniques. The CNNVAE feature embedding and graph construction requires no labeled data, which reduces overfitting and improves the generalization performance of graph learning at low label rates. Furthermore, the method easily incorporates a human-in-the-loop for active learning in the data-labeling process. We present promising results and compare them to other standard machine learning methods on the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset for ATR with small amounts of labeled data.

Efficient and Reliable Overlay Networks for Decentralized Federated Learning

We propose near-optimal overlay networks based on $d$-regular expander graphs to accelerate decentralized federated learning (DFL) and improve its generalization. In DFL a massive number of clients are connected by an overlay network, and they solve machine learning problems collaboratively without sharing raw data. Our overlay network design integrates spectral graph theory and the theoretical convergence and generalization bounds for DFL. As such, our proposed overlay networks accelerate convergence, improve generalization, and enhance robustness to clients failures in DFL with theoretical guarantees. Also, we present an efficient algorithm to convert a given graph to a practical overlay network and maintaining the network topology after potential client failures. We numerically verify the advantages of DFL with our proposed networks on various benchmark tasks, ranging from image classification to language modeling using hundreds of clients.

Model-Change Active Learning in Graph-Based Semi-Supervised Learning

Active learning in semi-supervised classification involves introducing additional labels for unlabelled data to improve the accuracy of the underlying classifier. A challenge is to identify which points to label to best improve performance while limiting the number of new labels. "Model-change" active learning quantifies the resulting change incurred in the classifier by introducing the additional label(s). We pair this idea with graph-based semi-supervised learning methods, that use the spectrum of the graph Laplacian matrix, which can be truncated to avoid prohibitively large computational and storage costs. We consider a family of convex loss functions for which the acquisition function can be efficiently approximated using the Laplace approximation of the posterior distribution. We show a variety of multiclass examples that illustrate improved performance over prior state-of-art.

Posterior Consistency of Semi-Supervised Regression on Graphs

Graph-based semi-supervised regression (SSR) is the problem of estimating the value of a function on a weighted graph from its values (labels) on a small subset of the vertices. This paper is concerned with the consistency of SSR in the context of classification, in the setting where the labels have small noise and the underlying graph weighting is consistent with well-clustered nodes. We present a Bayesian formulation of SSR in which the weighted graph defines a Gaussian prior, using a graph Laplacian, and the labeled data defines a likelihood. We analyze the rate of contraction of the posterior measure around the ground truth in terms of parameters that quantify the small label error and inherent clustering in the graph. We obtain bounds on the rates of contraction and illustrate their sharpness through numerical experiments. The analysis also gives insight into the choice of hyperparameters that enter the definition of the prior.

Efficient Graph-Based Active Learning with Probit Likelihood via Gaussian Approximations

We present a novel adaptation of active learning to graph-based semi-supervised learning (SSL) under non-Gaussian Bayesian models. We present an approximation of non-Gaussian distributions to adapt previously Gaussian-based acquisition functions to these more general cases. We develop an efficient rank-one update for applying "look-ahead" based methods as well as model retraining. We also introduce a novel "model change" acquisition function based on these approximations that further expands the available collection of active learning acquisition functions for such methods.