Diffusion models are recently employed as generative classifiers for robust classification. However, a comprehensive theoretical understanding of the robustness of diffusion classifiers is still lacking, leading us to question whether they will be vulnerable to future stronger attacks. In this study, we propose a new family of diffusion classifiers, named Noised Diffusion Classifiers~(NDCs), that possess state-of-the-art certified robustness. Specifically, we generalize the diffusion classifiers to classify Gaussian-corrupted data by deriving the evidence lower bounds (ELBOs) for these distributions, approximating the likelihood using the ELBO, and calculating classification probabilities via Bayes' theorem. We integrate these generalized diffusion classifiers with randomized smoothing to construct smoothed classifiers possessing non-constant Lipschitzness. Experimental results demonstrate the superior certified robustness of our proposed NDCs. Notably, we are the first to achieve 80\%+ and 70\%+ certified robustness on CIFAR-10 under adversarial perturbations with $\ell_2$ norm less than 0.25 and 0.5, respectively, using a single off-the-shelf diffusion model without any additional data.

Initial weighting is significant in deep neural networks because the random selection of weights produces different outputs and increases the probability of overfitting and underfitting. On the other hand, vector-based approaches to extract vector features need rich vectors for more accurate classification. The InceptionCapsule approach is presented to alleviate these two problems. This approach uses transfer learning and the Inception-ResNet model to avoid random selection of weights, which takes initial weights from ImageNet. It also uses the output of Inception middle layers to generate rich vectors. Extracted vectors are given to a capsule network for learning, which is equipped with an attention technique. Kvasir data and BUSI with the GT dataset were used to evaluate this approach. This model was able to achieve 97.62 accuracies in 5-class classification and also achieved 94.30 accuracies in 8-class classification on Kvasir. In the BUSI with GT dataset, the proposed approach achieved accuracy=98.88, Precision=95.34, and F1-score=93.74, which are acceptable results compared to other approaches in the literature.

Background and objective: Diabetes is a chronic pathology which is affecting more and more people over the years. It gives rise to a large number of deaths each year. Furthermore, many people living with the disease do not realize the seriousness of their health status early enough. Late diagnosis brings about numerous health problems and a large number of deaths each year so the development of methods for the early diagnosis of this pathology is essential. Methods: In this paper, a pipeline based on deep learning techniques is proposed to predict diabetic people. It includes data augmentation using a variational autoencoder (VAE), feature augmentation using an sparse autoencoder (SAE) and a convolutional neural network for classification. Pima Indians Diabetes Database, which takes into account information on the patients such as the number of pregnancies, glucose or insulin level, blood pressure or age, has been evaluated. Results: A 92.31% of accuracy was obtained when CNN classifier is trained jointly the SAE for featuring augmentation over a well balanced dataset. This means an increment of 3.17% of accuracy with respect the state-of-the-art. Conclusions: Using a full deep learning pipeline for data preprocessing and classification has demonstrate to be very promising in the diabetes detection field outperforming the state-of-the-art proposals.

Recent diffusion models provide a promising zero-shot solution to noisy linear inverse problems without retraining for specific inverse problems. In this paper, we propose the first unified interpretation for existing zero-shot methods from the perspective of approximating the conditional posterior mean for the reverse diffusion process of conditional sampling. We reveal that recent methods are equivalent to making isotropic Gaussian approximations to intractable posterior distributions over clean images given diffused noisy images, with the only difference in the handcrafted design of isotropic posterior covariances. Inspired by this finding, we propose a general plug-and-play posterior covariance optimization based on maximum likelihood estimation to improve recent methods. To achieve optimal posterior covariance without retraining, we provide general solutions based on two approaches specifically designed to leverage pre-trained models with and without reverse covariances. Experimental results demonstrate that the proposed methods significantly enhance the overall performance or robustness to hyperparameters of recent methods. Code is available at https://github.com/xypeng9903/k-diffusion-inverse-problems

Privacy concerns have led to a surge in the creation of synthetic datasets, with diffusion models emerging as a promising avenue. Although prior studies have performed empirical evaluations on these models, there has been a gap in providing a mathematical characterization of their privacy-preserving capabilities. To address this, we present the pioneering theoretical exploration of the privacy preservation inherent in discrete diffusion models (DDMs) for discrete dataset generation. Focusing on per-instance differential privacy (pDP), our framework elucidates the potential privacy leakage for each data point in a given training dataset, offering insights into how the privacy loss of each point correlates with the dataset's distribution. Our bounds also show that training with $s$-sized data points leads to a surge in privacy leakage from $(\epsilon, O(\frac{1}{s^2\epsilon}))$-pDP to $(\epsilon, O(\frac{1}{s\epsilon}))$-pDP of the DDM during the transition from the pure noise to the synthetic clean data phase, and a faster decay in diffusion coefficients amplifies the privacy guarantee. Finally, we empirically verify our theoretical findings on both synthetic and real-world datasets.

This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input to a neural network that outputs a second, interdependent distribution. Starting from a simple prior and iteratively updating the two distributions yields a generative procedure similar to the reverse process of diffusion models; however it is conceptually simpler in that no forward process is required. Discrete and continuous-time loss functions are derived for continuous, discretised and discrete data, along with sample generation procedures. Notably, the network inputs for discrete data lie on the probability simplex, and are therefore natively differentiable, paving the way for gradient-based sample guidance and few-step generation in discrete domains such as language modelling. The loss function directly optimises data compression and places no restrictions on the network architecture. In our experiments BFNs achieve competitive log-likelihoods for image modelling on dynamically binarized MNIST and CIFAR-10, and outperform all known discrete diffusion models on the text8 character-level language modelling task.

Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling predictions of their temporal evolution and analyses of thermodynamic quantities, including absorbed heat, work done on the system, and entropy production. However, inferring the Langevin equation from observed trajectories remains challenging, particularly for nonlinear and high-dimensional systems. In this study, we present a comprehensive framework that employs Bayesian neural networks for inferring Langevin equations in both overdamped and underdamped regimes. Our framework first provides the drift force and diffusion matrix separately and then combines them to construct the Langevin equation. By providing a distribution of predictions instead of a single value, our approach allows us to assess prediction uncertainties, which can prevent potential misunderstandings and erroneous decisions about the system. We demonstrate the effectiveness of our framework in inferring Langevin equations for various scenarios including a neuron model and microscopic engine, highlighting its versatility and potential impact.

Kernel methods are widely used in machine learning, especially for classification problems. However, the theoretical analysis of kernel classification is still limited. This paper investigates the statistical performances of kernel classifiers. With some mild assumptions on the conditional probability $\eta(x)=\mathbb{P}(Y=1\mid X=x)$, we derive an upper bound on the classification excess risk of a kernel classifier using recent advances in the theory of kernel regression. We also obtain a minimax lower bound for Sobolev spaces, which shows the optimality of the proposed classifier. Our theoretical results can be extended to the generalization error of overparameterized neural network classifiers. To make our theoretical results more applicable in realistic settings, we also propose a simple method to estimate the interpolation smoothness of $2\eta(x)-1$ and apply the method to real datasets.

In such cases, transferring knowledge from the source domain becomes crucial, particularly because the Machine learning has made substantial advancements in limited initial data in the target domain may be insufficient recent decades, with its applications spanning a wide range of for effective learning. The extensive and diverse information fields such as image and speech recognition, natural language available from the source domains can significantly compensate processing, and autonomous driving. Despite these achievements, for this shortfall, providing a foundational knowledge base machine learning in biomedicine faces significant challenges, that the model can build upon as more target domain data particularly in data collection. The acquisition of labeled becomes available. Therefore, the efficiency and effectiveness data can be very costly or even unfeasible due to factors of learning in the target domain are greatly enhanced by the like ethical considerations, patient privacy, and the scarcity transferred knowledge from the source domains. of certain diseases. These challenges have led researchers to Online transfer learning entails leveraging knowledge from increasingly rely on utilizing data from related domains that a static source domain and applying it to an ongoing, evolving have a more abundant supply of data.

Causal discovery, the task of inferring causal structure from data, promises to accelerate scientific research, inform policy making, and more. However, the per-dataset nature of existing causal discovery algorithms renders them slow, data hungry, and brittle. Inspired by foundation models, we propose a causal discovery framework where a deep learning model is pretrained to resolve predictions from classical discovery algorithms run over smaller subsets of variables. This method is enabled by the observations that the outputs from classical algorithms are fast to compute for small problems, informative of (marginal) data structure, and their structure outputs as objects remain comparable across datasets. Our method achieves state-of-the-art performance on synthetic and realistic datasets, generalizes to data generating mechanisms not seen during training, and offers inference speeds that are orders of magnitude faster than existing models.