Vu Dinh

Cuong N. Nguyen, Lam Si Tung Ho, Vu Dinh et al.

We analyze new generalization bounds for deep learning models trained by transfer learning from a source to a target task. Our bounds utilize a quantity called the majority predictor accuracy, which can be computed efficiently from data. We show that our theory is useful in practice since it implies that the majority predictor accuracy can be used as a transferability measure, a fact that is also validated by our experiments.

Julian Rene Cuellar Buritica, Vu Dinh, Manjula Burri et al.

Previous studies on echocardiogram segmentation are focused on the left ventricle in parasternal long-axis views. In this study, deep-learning models were evaluated on the segmentation of the ventricles in parasternal short-axis echocardiograms (PSAX-echo). Segmentation of the ventricles in complementary echocardiogram views will allow the computation of important metrics with the potential to aid in diagnosing cardio-pulmonary diseases and other cardiomyopathies. Evaluating state-of-the-art models with small datasets can reveal if they improve performance on limited data. PSAX-echo were performed on 33 volunteer women. An experienced cardiologist identified end-diastole and end-systole frames from 387 scans, and expert observers manually traced the contours of the cardiac structures. Traced frames were pre-processed and used to create labels to train 2 specific-domain (Unet-Resnet101 and Unet-ResNet50), and 4 general-domain (3 Segment Anything (SAM) variants, and the Detectron2) deep-learning models. The performance of the models was evaluated using the Dice similarity coefficient (DSC), Hausdorff distance (HD), and difference in cross-sectional area (DCSA). The Unet-Resnet101 model provided superior performance in the segmentation of the ventricles with 0.83, 4.93 pixels, and 106 pixel2 on average for DSC, HD, and DCSA respectively. A fine-tuned MedSAM model provided a performance of 0.82, 6.66 pixels, and 1252 pixel2, while the Detectron2 model provided 0.78, 2.12 pixels, and 116 pixel2 for the same metrics respectively. Deep-learning models are suitable for the segmentation of the left and right ventricles in PSAX-echo. This study demonstrated that specific-domain trained models such as Unet-ResNet provide higher accuracy for echo segmentation than general-domain segmentation models when working with small and locally acquired datasets.

Lam Si Tung Ho, Binh T. Nguyen, Vu Dinh et al.

In this paper, we study the learning rate of generalized Bayes estimators in a general setting where the hypothesis class can be uncountable and have an irregular shape, the loss function can have heavy tails, and the optimal hypothesis may not be unique. We prove that under the multi-scale Bernstein's condition, the generalized posterior distribution concentrates around the set of optimal hypotheses and the generalized Bayes estimator can achieve fast learning rate. Our results are applied to show that the standard Bayesian linear regression is robust to heavy-tailed distributions.

Lam Si Tung Ho, Vu Dinh

Large neural network models have high predictive power but may suffer from overfitting if the training set is not large enough. Therefore, it is desirable to select an appropriate size for neural networks. The destructive approach, which starts with a large architecture and then reduces the size using a Lasso-type penalty, has been used extensively for this task. Despite its popularity, there is no theoretical guarantee for this technique. Based on the notion of minimal neural networks, we posit a rigorous mathematical framework for studying the asymptotic theory of the destructive technique. We prove that Adaptive group Lasso is consistent and can reconstruct the correct number of hidden nodes of one-hidden-layer feedforward networks with high probability. To the best of our knowledge, this is the first theoretical result establishing for the destructive technique.

Binh T. Nguyen, Duy M. Nguyen, Lam Si Tung Ho et al.

In this work, we introduce a novel method for solving the set inversion problem by formulating it as a binary classification problem. Aiming to develop a fast algorithm that can work effectively with high-dimensional and computationally expensive nonlinear models, we focus on active learning, a family of new and powerful techniques which can achieve the same level of accuracy with fewer data points compared to traditional learning methods. Specifically, we propose OASIS, an active learning framework using Support Vector Machine algorithms for solving the problem of set inversion. Our method works well in high dimensions and its computational cost is relatively robust to the increase of dimension. We illustrate the performance of OASIS by several simulation studies and show that our algorithm outperforms VISIA, the state-of-the-art method.

Vu Dinh, Lam Si Tung Ho

One of the most important steps toward interpretability and explainability of neural network models is feature selection, which aims to identify the subset of relevant features. Theoretical results in the field have mostly focused on the prediction aspect of the problem with virtually no work on feature selection consistency for deep neural networks due to the model's severe nonlinearity and unidentifiability. This lack of theoretical foundation casts doubt on the applicability of deep learning to contexts where correct interpretations of the features play a central role. In this work, we investigate the problem of feature selection for analytic deep networks. We prove that for a wide class of networks, including deep feed-forward neural networks, convolutional neural networks, and a major sub-class of residual neural networks, the Adaptive Group Lasso selection procedure with Group Lasso as the base estimator is selection-consistent. The work provides further evidence that Group Lasso might be inefficient for feature selection with neural networks and advocates the use of Adaptive Group Lasso over the popular Group Lasso.

Vu Dinh, Lam Si Tung Ho

One main obstacle for the wide use of deep learning in medical and engineering sciences is its interpretability. While neural network models are strong tools for making predictions, they often provide little information about which features play significant roles in influencing the prediction accuracy. To overcome this issue, many regularization procedures for learning with neural networks have been proposed for dropping non-significant features. Unfortunately, the lack of theoretical results casts doubt on the applicability of such pipelines. In this work, we propose and establish a theoretical guarantee for the use of the adaptive group lasso for selecting important features of neural networks. Specifically, we show that our feature selection method is consistent for single-output feed-forward neural networks with one hidden layer and hyperbolic tangent activation function. We demonstrate its applicability using both simulation and data analysis.

Cuong V. Nguyen, Lam Si Tung Ho, Huan Xu et al.

We study pool-based active learning with abstention feedbacks where a labeler can abstain from labeling a queried example with some unknown abstention rate. This is an important problem with many useful applications. We take a Bayesian approach to the problem and develop two new greedy algorithms that learn both the classification problem and the unknown abstention rate at the same time. These are achieved by simply incorporating the estimated average abstention rate into the greedy criteria. We prove that both algorithms have near-optimality guarantees: they respectively achieve a ${(1-\frac{1}{e})}$ constant factor approximation of the optimal expected or worst-case value of a useful utility function. Our experiments show the algorithms perform well in various practical scenarios.

Cheng Zhang, Vu Dinh, Frederick A. Matsen

Phylogenetic tree inference using deep DNA sequencing is reshaping our understanding of rapidly evolving systems, such as the within-host battle between viruses and the immune system. Densely sampled phylogenetic trees can contain special features, including "sampled ancestors" in which we sequence a genotype along with its direct descendants, and "polytomies" in which multiple descendants arise simultaneously. These features are apparent after identifying zero-length branches in the tree. However, current maximum-likelihood based approaches are not capable of revealing such zero-length branches. In this paper, we find these zero-length branches by introducing adaptive-LASSO-type regularization estimators to phylogenetics, deriving their properties, and showing regularization to be a practically useful approach for phylogenetics.

Cuong V. Nguyen, Lam Si Tung Ho, Huan Xu et al.

We study pool-based active learning with abstention feedbacks, where a labeler can abstain from labeling a queried example with some unknown abstention rate. This is an important problem with many useful applications. We take a Bayesian approach to the problem and develop two new greedy algorithms that learn both the classification problem and the unknown abstention rate at the same time. These are achieved by simply incorporating the estimated abstention rate into the greedy criteria. We prove that both of our algorithms have near-optimality guarantees: they respectively achieve a ${(1-\frac{1}{e})}$ constant factor approximation of the optimal expected or worst-case value of a useful utility function. Our experiments show the algorithms perform well in various practical scenarios.

Vu Dinh, Lam Si Tung Ho, Duy Nguyen et al.

We study fast learning rates when the losses are not necessarily bounded and may have a distribution with heavy tails. To enable such analyses, we introduce two new conditions: (i) the envelope function $\sup_{f \in \mathcal{F}}|\ell \circ f|$, where $\ell$ is the loss function and $\mathcal{F}$ is the hypothesis class, exists and is $L^r$-integrable, and (ii) $\ell$ satisfies the multi-scale Bernstein's condition on $\mathcal{F}$. Under these assumptions, we prove that learning rate faster than $O(n^{-1/2})$ can be obtained and, depending on $r$ and the multi-scale Bernstein's powers, can be arbitrarily close to $O(n^{-1})$. We then verify these assumptions and derive fast learning rates for the problem of vector quantization by $k$-means clustering with heavy-tailed distributions. The analyses enable us to obtain novel learning rates that extend and complement existing results in the literature from both theoretical and practical viewpoints.

Vu Dinh, Lam Si Tung Ho, Nguyen Viet Cuong et al.

We prove new fast learning rates for the one-vs-all multiclass plug-in classifiers trained either from exponentially strongly mixing data or from data generated by a converging drifting distribution. These are two typical scenarios where training data are not iid. The learning rates are obtained under a multiclass version of Tsybakov's margin assumption, a type of low-noise assumption, and do not depend on the number of classes. Our results are general and include a previous result for binary-class plug-in classifiers with iid data as a special case. In contrast to previous works for least squares SVMs under the binary-class setting, our results retain the optimal learning rate in the iid case.

Nguyen Viet Cuong, Lam Si Tung Ho, Vu Dinh

We analyze the generalization and robustness of the batched weighted average algorithm for V-geometrically ergodic Markov data. This algorithm is a good alternative to the empirical risk minimization algorithm when the latter suffers from overfitting or when optimizing the empirical risk is hard. For the generalization of the algorithm, we prove a PAC-style bound on the training sample size for the expected $L_1$-loss to converge to the optimal loss when training data are V-geometrically ergodic Markov chains. For the robustness, we show that if the training target variable's values contain bounded noise, then the generalization bound of the algorithm deviates at most by the range of the noise. Our results can be applied to the regression problem, the classification problem, and the case where there exists an unknown deterministic target hypothesis.