In recent years, diffusion models, and more generally score-based deep generative models, have achieved remarkable success in various applications, including image and audio generation. In this paper, we view diffusion models as an implicit approach to nonparametric density estimation and study them within a statistical framework to analyze their surprising performance. A key challenge in high-dimensional statistical inference is leveraging low-dimensional structures inherent in the data to mitigate the curse of dimensionality. We assume that the underlying density exhibits a low-dimensional structure by factorizing into low-dimensional components, a property common in examples such as Bayesian networks and Markov random fields. Under suitable assumptions, we demonstrate that an implicit density estimator constructed from diffusion models adapts to the factorization structure and achieves the minimax optimal rate with respect to the total variation distance. In constructing the estimator, we design a sparse weight-sharing neural network architecture, where sparsity and weight-sharing are key features of practical architectures such as convolutional neural networks and recurrent neural networks.

Goal-oriented chatbots are essential for automating user tasks, such as booking flights or making restaurant reservations. A key component of these systems is Dialogue State Tracking (DST), which interprets user intent and maintains the dialogue state. However, existing DST methods often rely on fixed ontologies and manually compiled slot values, limiting their adaptability to open-domain dialogues. We propose a novel approach that leverages instruction tuning and advanced prompt strategies to enhance DST performance, without relying on any predefined ontologies. Our method enables Large Language Model (LLM) to infer dialogue states through carefully designed prompts and includes an anti-hallucination mechanism to ensure accurate tracking in diverse conversation contexts. Additionally, we employ a Variational Graph Auto-Encoder (VGAE) to model and predict subsequent user intent. Our approach achieved state-of-the-art with a JGA of 42.57% outperforming existing ontology-less DST models, and performed well in open-domain real-world conversations. This work presents a significant advancement in creating more adaptive and accurate goal-oriented chatbots.

Quantum convolutional neural networks (QCNNs) represent a promising approach in quantum machine learning, paving new directions for both quantum and classical data analysis. This approach is particularly attractive due to the absence of the barren plateau problem, a fundamental challenge in training quantum neural networks (QNNs), and its feasibility. However, a limitation arises when applying QCNNs to classical data. The network architecture is most natural when the number of input qubits is a power of two, as this number is reduced by a factor of two in each pooling layer. The number of input qubits determines the dimensions (i.e. the number of features) of the input data that can be processed, restricting the applicability of QCNN algorithms to real-world data. To address this issue, we propose a QCNN architecture capable of handling arbitrary input data dimensions while optimizing the allocation of quantum resources such as ancillary qubits and quantum gates. This optimization is not only important for minimizing computational resources, but also essential in noisy intermediate-scale quantum (NISQ) computing, as the size of the quantum circuits that can be executed reliably is limited. Through numerical simulations, we benchmarked the classification performance of various QCNN architectures when handling arbitrary input data dimensions on the MNIST and Breast Cancer datasets. The results validate that the proposed QCNN architecture achieves excellent classification performance while utilizing a minimal resource overhead, providing an optimal solution when reliable quantum computation is constrained by noise and imperfections.

Identifying whether a given sample is an outlier or not is an important issue in various real-world domains. This study aims to solve the unsupervised outlier detection problem where training data contain outliers, but any label information about inliers and outliers is not given. We propose a powerful and efficient learning framework to identify outliers in a training data set using deep neural networks. We start with a new observation called the inlier-memorization (IM) effect. When we train a deep generative model with data contaminated with outliers, the model first memorizes inliers before outliers. Exploiting this finding, we develop a new method called the outlier detection via the IM effect (ODIM). The ODIM only requires a few updates; thus, it is computationally efficient, tens of times faster than other deep-learning-based algorithms. Also, the ODIM filters out outliers successfully, regardless of the types of data, such as tabular, image, and sequential. We empirically demonstrate the superiority and efficiency of the ODIM by analyzing 20 data sets.

As they have a vital effect on social decision-making, AI algorithms should be not only accurate but also fair. Among various algorithms for fairness AI, learning fair representation (LFR), whose goal is to find a fair representation with respect to sensitive variables such as gender and race, has received much attention. For LFR, the adversarial training scheme is popularly employed as is done in the generative adversarial network type algorithms. The choice of a discriminator, however, is done heuristically without justification. In this paper, we propose a new adversarial training scheme for LFR, where the integral probability metric (IPM) with a specific parametric family of discriminators is used. The most notable result of the proposed LFR algorithm is its theoretical guarantee about the fairness of the final prediction model, which has not been considered yet. That is, we derive theoretical relations between the fairness of representation and the fairness of the prediction model built on the top of the representation (i.e., using the representation as the input). Moreover, by numerical experiments, we show that our proposed LFR algorithm is computationally lighter and more stable, and the final prediction model is competitive or superior to other LFR algorithms using more complex discriminators.

In many classification problems, collecting massive clean-annotated data is not easy, and thus a lot of researches have been done to handle data with noisy labels. Most recent state-of-art solutions for noisy label problems are built on the small-loss strategy which exploits the memorization effect. While it is a powerful tool, the memorization effect has several drawbacks. The performances are sensitive to the choice of a training epoch required for utilizing the memorization effect. In addition, when the labels are heavily contaminated or imbalanced, the memorization effect may not occur in which case the methods based on the small-loss strategy fail to identify clean labeled data. We introduce a new method called INN(Integration with the Nearest Neighborhoods) to refine clean labeled data from training data with noisy labels. The proposed method is based on a new discovery that a prediction pattern at neighbor regions of clean labeled data is consistently different from that of noisy labeled data regardless of training epochs. The INN method requires more computation but is much stable and powerful than the small-loss strategy. By carrying out various experiments, we demonstrate that the INN method resolves the shortcomings in the memorization effect successfully and thus is helpful to construct more accurate deep prediction models with training data with noisy labels.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure such as a low-dimensional manifold is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

In semi-supervised learning, virtual adversarial training (VAT) approach is one of the most attractive method due to its intuitional simplicity and powerful performances. VAT finds a classifier which is robust to data perturbation toward the adversarial direction. In this study, we provide a fundamental explanation why VAT works well in semi-supervised learning case and propose new techniques which are simple but powerful to improve the VAT method. Especially we employ the idea of Bad GAN approach, which utilizes bad samples distributed on complement of the support of the input data, without any additional deep generative architectures. We generate bad samples of high-quality by use of the adversarial training used in VAT and also give theoretical explanations why the adversarial training is good at both generating bad samples. An advantage of our proposed method is to achieve the competitive performances compared with other recent studies with much fewer computations. We demonstrate advantages our method by various experiments with well known benchmark image datasets.

We derive the fast convergence rates of a deep neural network (DNN) classifier with the rectified linear unit (ReLU) activation function learned using the hinge loss. We consider three cases for a true model: (1) a smooth decision boundary, (2) smooth conditional class probability, and (3) the margin condition (i.e., the probability of inputs near the decision boundary is small). We show that the DNN classifier learned using the hinge loss achieves fast rate convergences for all three cases provided that the architecture (i.e., the number of layers, number of nodes and sparsity). is carefully selected. An important implication is that DNN architectures are very flexible for use in various cases without much modification. In addition, we consider a DNN classifier learned by minimizing the cross-entropy, and show that the DNN classifier achieves a fast convergence rate under the condition that the conditional class probabilities of most data are sufficiently close to either 1 or zero. This assumption is not unusual for image recognition because human beings are extremely good at recognizing most images. To confirm our theoretical explanation, we present the results of a small numerical study conducted to compare the hinge loss and cross-entropy.

We provide a theoretical explanation of the role of the number of nodes at each layer in deep neural networks. We prove that the largest variation of a deep neural network with ReLU activation function arises when the layer with the fewest nodes changes its activation pattern. An important implication is that deep neural network is a useful tool to generate functions most of whose variations are concentrated on a smaller area of the input space near the boundaries corresponding to the layer with the fewest nodes. In turn, this property makes the function more invariant to input transformation. That is, our theoretical result gives a clue about how to design the architecture of a deep neural network to increase complexity and transformation invariancy simultaneously.