Haoyin Xu

Jayanta Dey, Haoyin Xu, Ashwin De Silva et al.

Deep discriminative approaches, such as decision forests and deep neural networks, have recently found applications in many important real-world scenarios. However, deploying these learning algorithms in safety-critical applications raises concerns, particularly when it comes to ensuring calibration for both in-distribution and out-of-distribution regions. Many popular methods for in-distribution (ID) calibration, such as isotonic and Platt's sigmoidal regression, exhibit adequate ID calibration performance. However, these methods are not calibrated for the entire feature space, leading to overconfidence in the out-of-distribution (OOD) region. Existing OOD calibration methods generally exhibit poor ID calibration. In this paper, we jointly address the ID and OOD problems. We leveraged the fact that deep models learn to partition feature space into a union of polytopes, that is, flat-sided geometric objects. We introduce a geodesic distance to measure the distance between these polytopes and further distinguish samples within the same polytope using a Gaussian kernel. Our experiments on both tabular and vision benchmarks show that the proposed approaches, namely Kernel Density Forest (KDF) and Kernel Density Network (KDN), obtain well-calibrated posteriors for both ID and OOD samples, while mostly preserving the classification accuracy and extrapolating beyond the training data to handle OOD inputs appropriately.

Haoyin Xu, Jayanta Dey, Sambit Panda et al.

Decision forests, including random forests and gradient boosting trees, remain the leading machine learning methods for many real-world data problems, especially on tabular data. However, most of the current implementations only operate in batch mode, and therefore cannot incrementally update when more data arrive. Several previous works developed streaming trees and ensembles to overcome this limitation. Nonetheless, we found that those state-of-the-art algorithms suffer from a number of drawbacks, including low accuracy on some problems and high memory usage on others. We therefore developed an extremely simple extension of decision trees: given new data, simply update existing trees by continuing to grow them, and replace some old trees with new ones to control the total number of trees. In a benchmark suite containing 72 classification problems (the OpenML-CC18 data suite), we illustrate that our approach, $\textit{Extremely Simple Streaming Forest}$ (XForest), does not suffer from either of the aforementioned limitations. On those datasets, we also demonstrate that our approach often performs as well as, and sometimes even better than, conventional batch decision forest algorithms. With a $\textit{zero-added-node}$ approach, XForest-Zero, we also further extend existing splits to new tasks, and this very efficient method only requires inference time. Thus, XForests establish a simple standard for streaming trees and forests that could readily be applied to many real-world problems.

Jayanta Dey, Ali Geisa, Ronak Mehta et al.

Learning is a process wherein a learning agent enhances its performance through exposure of experience or data. Throughout this journey, the agent may encounter diverse learning environments. For example, data may be presented to the leaner all at once, in multiple batches, or sequentially. Furthermore, the distribution of each data sample could be either identical and independent (iid) or non-iid. Additionally, there may exist computational and space constraints for the deployment of the learning algorithms. The complexity of a learning task can vary significantly, depending on the learning setup and the constraints imposed upon it. However, it is worth noting that the current literature lacks formal definitions for many of the in-distribution and out-of-distribution learning paradigms. Establishing proper and universally agreed-upon definitions for these learning setups is essential for thoroughly exploring the evolution of ideas across different learning scenarios and deriving generalized mathematical bounds for these learners. In this paper, we aim to address this issue by proposing a chronological approach to defining different learning tasks using the provably approximately correct (PAC) learning framework. We will start with in-distribution learning and progress to recently proposed lifelong or continual learning. We employ consistent terminology and notation to demonstrate how each of these learning frameworks represents a specific instance of a broader, more generalized concept of learnability. Our hope is that this work will inspire a universally agreed-upon approach to quantifying different types of learning, fostering greater understanding and progress in the field.

Haoyin Xu, Kaleab A. Kinfu, Will LeVine et al.

Deep networks and decision forests (such as random forests and gradient boosted trees) are the leading machine learning methods for structured and tabular data, respectively. Many papers have empirically compared large numbers of classifiers on one or two different domains (e.g., on 100 different tabular data settings). However, a careful conceptual and empirical comparison of these two strategies using the most contemporary best practices has yet to be performed. Conceptually, we illustrate that both can be profitably viewed as "partition and vote" schemes. Specifically, the representation space that they both learn is a partitioning of feature space into a union of convex polytopes. For inference, each decides on the basis of votes from the activated nodes. This formulation allows for a unified basic understanding of the relationship between these methods. Empirically, we compare these two strategies on hundreds of tabular data settings, as well as several vision and auditory settings. Our focus is on datasets with at most 10,000 samples, which represent a large fraction of scientific and biomedical datasets. In general, we found forests to excel at tabular and structured data (vision and audition) with small sample sizes, whereas deep nets performed better on structured data with larger sample sizes. This suggests that further gains in both scenarios may be realized via further combining aspects of forests and networks. We will continue revising this technical report in the coming months with updated results.

Jayanta Dey, Joshua T. Vogelstein, Hayden S. Helm et al.

In lifelong learning, data are used to improve performance not only on the present task, but also on past and future (unencountered) tasks. While typical transfer learning algorithms can improve performance on future tasks, their performance on prior tasks degrades upon learning new tasks (called forgetting). Many recent approaches for continual or lifelong learning have attempted to maintain performance on old tasks given new tasks. But striving to avoid forgetting sets the goal unnecessarily low. The goal of lifelong learning should be to use data to improve performance on both future tasks (forward transfer) and past tasks (backward transfer). In this paper, we show that a simple approach -- representation ensembling -- demonstrates both forward and backward transfer in a variety of simulated and benchmark data scenarios, including tabular, vision (CIFAR-100, 5-dataset, Split Mini-Imagenet, and Food1k), and speech (spoken digit), in contrast to various reference algorithms, which typically failed to transfer either forward or backward, or both. Moreover, our proposed approach can flexibly operate with or without a computational budget.