Node classification with Graph Neural Networks (GNN) under a fixed set of labels is well known in contrast to Graph Few-Shot Class Incremental Learning (GFSCIL), which involves learning a GNN classifier as graph nodes and classes growing over time sporadically. We introduce inductive GFSCIL that continually learns novel classes with newly emerging nodes while maintaining performance on old classes without accessing previous data. This addresses the practical concern of transductive GFSCIL, which requires storing the entire graph with historical data. Compared to the transductive GFSCIL, the inductive setting exacerbates catastrophic forgetting due to inaccessible previous data during incremental training, in addition to overfitting issue caused by label sparsity. Thus, we propose a novel method, called Topology-based class Augmentation and Prototype calibration (TAP). To be specific, it first creates a triple-branch multi-topology class augmentation method to enhance model generalization ability. As each incremental session receives a disjoint subgraph with nodes of novel classes, the multi-topology class augmentation method helps replicate such a setting in the base session to boost backbone versatility. In incremental learning, given the limited number of novel class samples, we propose an iterative prototype calibration to improve the separation of class prototypes. Furthermore, as backbone fine-tuning poses the feature distribution drift, prototypes of old classes start failing over time, we propose the prototype shift method for old classes to compensate for the drift. We showcase the proposed method on four datasets.

We consider training decision trees using noisily labeled data, focusing on loss functions that can lead to robust learning algorithms. Our contributions are threefold. First, we offer novel theoretical insights on the robustness of many existing loss functions in the context of decision tree learning. We show that some of the losses belong to a class of what we call conservative losses, and the conservative losses lead to an early stopping behavior during training and noise-tolerant predictions during testing. Second, we introduce a framework for constructing robust loss functions, called distribution losses. These losses apply percentile-based penalties based on an assumed margin distribution, and they naturally allow adapting to different noise rates via a robustness parameter. In particular, we introduce a new loss called the negative exponential loss, which leads to an efficient greedy impurity-reduction learning algorithm. Lastly, our experiments on multiple datasets and noise settings validate our theoretical insight and the effectiveness of our adaptive negative exponential loss.

The Partially Observable Markov Decision Process (POMDP) provides a principled framework for decision making in stochastic partially observable environments. However, computing good solutions for problems with continuous action spaces remains challenging. To ease this challenge, we propose a simple online POMDP solver, called Lazy Cross-Entropy Search Over Policy Trees (LCEOPT). At each planning step, our method uses a novel lazy Cross-Entropy method to search the space of policy trees, which provide a simple policy representation. Specifically, we maintain a distribution on promising finite-horizon policy trees. The distribution is iteratively updated by sampling policies, evaluating them via Monte Carlo simulation, and refitting them to the top-performing ones. Our method is lazy in the sense that it exploits the policy tree representation to avoid redundant computations in policy sampling, evaluation, and distribution update. This leads to computational savings of up to two orders of magnitude. Our LCEOPT is surprisingly simple as compared to existing state-of-the-art methods, yet empirically outperforms them on several continuous-action POMDP problems, particularly for problems with higher-dimensional action spaces.

Supervised deep learning methods have shown promise in undersampled Magnetic Resonance Imaging (MRI) reconstruction, but their requirement for paired data limits their generalizability to the diverse MRI acquisition parameters. Recently, unsupervised controllable generative diffusion models have been applied to undersampled MRI reconstruction, without paired data or model retraining for different MRI acquisitions. However, diffusion models are generally slow in sampling and state-of-the-art acceleration techniques can lead to sub-optimal results when directly applied to the controllable generation process. This study introduces a new algorithm called Predictor-Projector-Noisor (PPN), which enhances and accelerates controllable generation of diffusion models for undersampled MRI reconstruction. Our results demonstrate that PPN produces high-fidelity MR images that conform to undersampled k-space measurements with significantly shorter reconstruction time than other controllable sampling methods. In addition, the unsupervised PPN accelerated diffusion models are adaptable to different MRI acquisition parameters, making them more practical for clinical use than supervised learning techniques.

Solving continuous Partially Observable Markov Decision Processes (POMDPs) is challenging, particularly for high-dimensional continuous action spaces. To alleviate this difficulty, we propose a new sampling-based online POMDP solver, called Adaptive Discretization using Voronoi Trees (ADVT). It uses Monte Carlo Tree Search in combination with an adaptive discretization of the action space as well as optimistic optimization to efficiently sample high-dimensional continuous action spaces and compute the best action to perform. Specifically, we adaptively discretize the action space for each sampled belief using a hierarchical partition called Voronoi tree, which is a Binary Space Partitioning that implicitly maintains the partition of a cell as the Voronoi diagram of two points sampled from the cell. ADVT uses the estimated diameters of the cells to form an upper-confidence bound on the action value function within the cell, guiding the Monte Carlo Tree Search expansion and further discretization of the action space. This enables ADVT to better exploit local information with respect to the action value function, allowing faster identification of the most promising regions in the action space, compared to existing solvers. Voronoi trees keep the cost of partitioning and estimating the diameter of each cell low, even in high-dimensional spaces where many sampled points are required to cover the space well. ADVT additionally handles continuous observation spaces, by adopting an observation progressive widening strategy, along with a weighted particle representation of beliefs. Experimental results indicate that ADVT scales substantially better to high-dimensional continuous action spaces, compared to state-of-the-art methods.

Positive-unlabeled (PU) learning deals with binary classification problems when only positive (P) and unlabeled (U) data are available. Many recent PU methods are based on neural networks, but little has been done to develop boosting algorithms for PU learning, despite boosting algorithms' strong performance on many fully supervised classification problems. In this paper, we propose a novel boosting algorithm, AdaPU, for PU learning. Similarly to AdaBoost, AdaPU aims to optimize an empirical exponential loss, but the loss is based on the PU data, rather than on positive-negative (PN) data. As in AdaBoost, we learn a weighted combination of weak classifiers by learning one weak classifier and its weight at a time. However, AdaPU requires a very different algorithm for learning the weak classifiers and determining their weights. This is because AdaPU learns a weak classifier and its weight using a weighted positive-negative (PN) dataset with some negative data weights $-$ the dataset is derived from the original PU data, and the data weights are determined by the current weighted classifier combination, but some data weights are negative. Our experiments showed that AdaPU outperforms neural networks on several benchmark PU datasets, including a large-scale challenging cyber security dataset.

Multiple-Intent Inverse Reinforcement Learning (MI-IRL) seeks to find a reward function ensemble to rationalize demonstrations of different but unlabelled intents. Within the popular expectation maximization (EM) framework for learning probabilistic MI-IRL models, we present a warm-start strategy based on up-front clustering of the demonstrations in feature space. Our theoretical analysis shows that this warm-start solution produces a near-optimal reward ensemble, provided the behavior modes satisfy mild separation conditions. We also propose a MI-IRL performance metric that generalizes the popular Expected Value Difference measure to directly assesses learned rewards against the ground-truth reward ensemble. Our metric elegantly addresses the difficulty of pairing up learned and ground truth rewards via a min-cost flow formulation, and is efficiently computable. We also develop a MI-IRL benchmark problem that allows for more comprehensive algorithmic evaluations. On this problem, we find our MI-IRL warm-start strategy helps avoid poor quality local minima reward ensembles, resulting in a significant improvement in behavior clustering. Our extensive sensitivity analysis demonstrates that the quality of the learned reward ensembles is improved under various settings, including cases where our theoretical assumptions do not necessarily hold. Finally, we demonstrate the effectiveness of our methods by discovering distinct driving styles in a large real-world dataset of driver GPS trajectories.

The problem of learning an optimal convex combination of basis models has been studied in a number of works, with a focus on the theoretical analysis, but little investigati on on the empirical performance of the approach. In this paper, we present some new theoretical insights, and empirical resul ts that demonstrate the effectiveness of the approach. Theore ti-cally, we first consider whether we can replace convex combinations by linear combinations, and obtain convergence r e-sults similar to existing results for learning from a convex hull. We present a negative result showing that the linear hull of very simple basis functions can have unbounded capacity, an d is thus prone to overfitting. On the other hand, convex hulls are still rich but have bounded capacities. In addition, we o b-tain a generalization bound for a general class of Lipschitz loss functions. Empirically, we first discuss how a convex combination can be greedily learned with early stopping, an d how a convex combination can be non-greedily learned when the number of basis models is known a priori. Our experiments suggest that the greedy scheme is competitive with or better than several baselines, including boosting and rand om forests. The greedy algorithm requires little effort in hyp er-parameter tuning, and also seems to adapt to the underlying complexity of the problem.

The partially observable Markov decision process (POMDP) provides a principled general framework for planning under uncertainty, but solving POMDPs optimally is computationally intractable, due to the "curse of dimensionality" and the "curse of history". To overcome these challenges, we introduce the Determinized Sparse Partially Observable Tree (DESPOT), a sparse approximation of the standard belief tree, for online planning under uncertainty. A DESPOT focuses online planning on a set of randomly sampled scenarios and compactly captures the "execution" of all policies under these scenarios. We show that the best policy obtained from a DESPOT is near-optimal, with a regret bound that depends on the representation size of the optimal policy. Leveraging this result, we give an anytime online planning algorithm, which searches a DESPOT for a policy that optimizes a regularized objective function. Regularization balances the estimated value of a policy under the sampled scenarios and the policy size, thus avoiding overfitting. The algorithm demonstrates strong experimental results, compared with some of the best online POMDP algorithms available. It has also been incorporated into an autonomous driving system for real-time vehicle control. The source code for the algorithm is available online.

We study the robustness of active learning (AL) algorithms against prior misspecification: whether an algorithm achieves similar performance using a perturbed prior as compared to using the true prior. In both the average and worst cases of the maximum coverage setting, we prove that all alpha-approximate algorithms are robust (i.e., near alpha-approximate) if the utility is Lipschitz continuous in the prior. We further show that robustness may not be achieved if the utility is non-Lipschitz. This suggests we should use a Lipschitz utility for AL if robustness is required. For the minimum cost setting, we can also obtain a robustness result for approximate AL algorithms. Our results imply that many commonly used AL algorithms are robust against perturbed priors. We then propose the use of a mixture prior to alleviate the problem of prior misspecification. We analyze the robustness of the uniform mixture prior and show experimentally that it performs reasonably well in practice.