Injecting heavy-tailed noise to the iterates of stochastic gradient descent (SGD) has received increasing attention over the past few years. While various theoretical properties of the resulting algorithm have been analyzed mainly from learning theory and optimization perspectives, their privacy preservation properties have not yet been established. Aiming to bridge this gap, we provide differential privacy (DP) guarantees for noisy SGD, when the injected noise follows an $\alpha$-stable distribution, which includes a spectrum of heavy-tailed distributions (with infinite variance) as well as the Gaussian distribution. Considering the $(\epsilon, \delta)$-DP framework, we show that SGD with heavy-tailed perturbations achieves $(0, \tilde{\mathcal{O}}(1/n))$-DP for a broad class of loss functions which can be non-convex, where $n$ is the number of data points. As a remarkable byproduct, contrary to prior work that necessitates bounded sensitivity for the gradients or clipping the iterates, our theory reveals that under mild assumptions, such a projection step is not actually necessary. We illustrate that the heavy-tailed noising mechanism achieves similar DP guarantees compared to the Gaussian case, which suggests that it can be a viable alternative to its light-tailed counterparts.
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Images captured from the real world are often affected by different types of noise, which can significantly impact the performance of Computer Vision systems and the quality of visual data. This study presents a novel approach for defect detection in casting product noisy images, specifically focusing on submersible pump impellers. The methodology involves utilizing deep learning models such as VGG16, InceptionV3, and other models in both the spatial and frequency domains to identify noise types and defect status. The research process begins with preprocessing images, followed by applying denoising techniques tailored to specific noise categories. The goal is to enhance the accuracy and robustness of defect detection by integrating noise detection and denoising into the classification pipeline. The study achieved remarkable results using VGG16 for noise type classification in the frequency domain, achieving an accuracy of over 99%. Removal of salt and pepper noise resulted in an average SSIM of 87.9, while Gaussian noise removal had an average SSIM of 64.0, and periodic noise removal yielded an average SSIM of 81.6. This comprehensive approach showcases the effectiveness of the deep AutoEncoder model and median filter, for denoising strategies in real-world industrial applications. Finally, our study reports significant improvements in binary classification accuracy for defect detection compared to previous methods. For the VGG16 classifier, accuracy increased from 94.6% to 97.0%, demonstrating the effectiveness of the proposed noise detection and denoising approach. Similarly, for the InceptionV3 classifier, accuracy improved from 84.7% to 90.0%, further validating the benefits of integrating noise analysis into the classification pipeline.
Semi-competing risks refers to the survival analysis setting where the occurrence of a non-terminal event is subject to whether a terminal event has occurred, but not vice versa. Semi-competing risks arise in a broad range of clinical contexts, with a novel example being the pregnancy condition preeclampsia, which can only occur before the `terminal' event of giving birth. Models that acknowledge semi-competing risks enable investigation of relationships between covariates and the joint timing of the outcomes, but methods for model selection and prediction of semi-competing risks in high dimensions are lacking. Instead, researchers commonly analyze only a single or composite outcome, losing valuable information and limiting clinical utility -- in the obstetric setting, this means ignoring valuable insight into timing of delivery after preeclampsia has onset. To address this gap we propose a novel penalized estimation framework for frailty-based illness-death multi-state modeling of semi-competing risks. Our approach combines non-convex and structured fusion penalization, inducing global sparsity as well as parsimony across submodels. We perform estimation and model selection via a pathwise routine for non-convex optimization, and prove the first statistical error bound results in this setting. We present a simulation study investigating estimation error and model selection performance, and a comprehensive application of the method to joint risk modeling of preeclampsia and timing of delivery using pregnancy data from an electronic health record.
Brain tumor growth is unique to each glioma patient and extends beyond what is visible in imaging scans, infiltrating surrounding brain tissue. Understanding these hidden patient-specific progressions is essential for effective therapies. Current treatment plans for brain tumors, such as radiotherapy, typically involve delineating a uniform margin around the visible tumor on pre-treatment scans to target this invisible tumor growth. This "one size fits all" approach is derived from population studies and often fails to account for the nuances of individual patient conditions. We present the GliODIL framework, which infers the full spatial distribution of tumor cell concentration from available multi-modal imaging, leveraging a Fisher-Kolmogorov type physics model to describe tumor growth. This is achieved through the newly introduced method of Optimizing the Discrete Loss (ODIL), where both data and physics-based constraints are softly assimilated into the solution. Our test dataset comprises 152 glioblastoma patients with pre-treatment imaging and post-treatment follow-ups for tumor recurrence monitoring. By blending data-driven techniques with physics-based constraints, GliODIL enhances recurrence prediction in radiotherapy planning, challenging traditional uniform margins and strict adherence to the Fisher-Kolmogorov partial differential equation (PDE) model, which is adapted for complex cases.
Recently it was shown that the response time of First-Come-First-Served (FCFS) scheduling can be stochastically and asymptotically improved upon by the {\it Nudge} scheduling algorithm in case of light-tailed job size distributions. Such improvements are feasible even when the jobs are partitioned into two types and the scheduler only has information about the type of incoming jobs (but not their size). In this paper we introduce Nudge-$M$ scheduling, where basically any incoming type-1 job is allowed to pass any type-2 job that is still waiting in the queue given that it arrived as one of the last $M$ jobs. We prove that Nudge-$M$ has an asymptotically optimal response time within a large family of Nudge scheduling algorithms when job sizes are light-tailed. Simple explicit results for the asymptotic tail improvement ratio (ATIR) of Nudge-$M$ over FCFS are derived as well as explicit results for the optimal parameter $M$. An expression for the ATIR that only depends on the type-1 and type-2 mean job sizes and the fraction of type-1 jobs is presented in the heavy traffic setting. The paper further presents a numerical method to compute the response time distribution and mean response time of Nudge-$M$ scheduling provided that the job size distribution of both job types follows a phase-type distribution (by making use of the framework of Markov modulated fluid queues with jumps).
PageRank is a widely used centrality measure that "ranks" vertices in a graph by considering the connections and their importance. In this report, we first introduce one of the most efficient GPU implementations of Static PageRank, which recomputes PageRank scores from scratch. It uses a synchronous pull-based atomics-free PageRank computation, with the low and high in-degree vertices being partitioned and processed by two separate kernels. Next, we present our GPU implementation of incrementally expanding (and contracting) Dynamic Frontier with Pruning (DF-P) PageRank, which processes only a subset of vertices likely to change ranks. It is based on Static PageRank, and uses an additional partitioning between low and high out-degree vertices for incremental expansion of the set of affected vertices with two additional kernels. On a server with an NVIDIA A100 GPU, our Static PageRank outperforms Hornet and Gunrock's PageRank implementations by 31x and 5.9x respectively. On top of the above, DF-P PageRank outperforms Static PageRank by 2.1x on real-world dynamic graphs, and by 3.1x on large static graphs with random batch updates.
Quadrotors have gained popularity over the last decade, aiding humans in complex tasks such as search and rescue, mapping and exploration. Despite their mechanical simplicity and versatility compared to other types of aerial vehicles, they remain vulnerable to rotor failures. In this paper, we propose an algorithmic and mechanical approach to addressing the quadrotor fault-tolerant problem in case of rotor failures. First, we present a fault-tolerant detection and control scheme that includes various attitude error metrics. The scheme transitions to a fault-tolerant control mode by surrendering the yaw control. Subsequently, to ensure compatibility with platform sensing constraints, we investigate the relationship between variations in robot rotational drag, achieved through a modular mechanical design appendage, resulting in yaw rates within sensor limits. This analysis offers a platform-agnostic framework for designing more reliable and robust quadrotors in the event of rotor failures. Extensive experimental results validate the proposed approach providing insights into successfully designing a cost-effective quadrotor capable of fault-tolerant control. The overall design enhances safety in scenarios of faulty rotors, without the need for additional sensors or computational resources.
The formulation of Mean Field Games (MFG) typically requires continuous differentiability of the Hamiltonian in order to determine the advective term in the Kolmogorov--Fokker--Planck equation for the density of players. However, in many cases of practical interest, the underlying optimal control problem may exhibit bang-bang controls, which typically lead to nondifferentiable Hamiltonians. We develop the analysis and numerical analysis of stationary MFG for the general case of convex, Lipschitz, but possibly nondifferentiable Hamiltonians. In particular, we propose a generalization of the MFG system as a Partial Differential Inclusion (PDI) based on interpreting the derivative of the Hamiltonian in terms of subdifferentials of convex functions. We establish existence of a weak solution to the MFG PDI system, and we further prove uniqueness under a similar monotonicity condition to the one considered by Lasry and Lions. We then propose a monotone finite element discretization of the problem, and we prove strong $H^1$-norm convergence of the approximations to the value function and strong $L^q$-norm convergence of the approximations of the density function. We illustrate the performance of the numerical method in numerical experiments featuring nonsmooth solutions.
In the literature on Kleene algebra, a number of variants have been proposed which impose additional structure specified by a theory, such as Kleene algebra with tests (KAT) and the recent Kleene algebra with observations (KAO), or make specific assumptions about certain constants, as for instance in NetKAT. Many of these variants fit within the unifying perspective offered by Kleene algebra with hypotheses, which comes with a canonical language model constructed from a given set of hypotheses. For the case of KAT, this model corresponds to the familiar interpretation of expressions as languages of guarded strings. A relevant question therefore is whether Kleene algebra together with a given set of hypotheses is complete with respect to its canonical language model. In this paper, we revisit, combine and extend existing results on this question to obtain tools for proving completeness in a modular way. We showcase these tools by giving new and modular proofs of completeness for KAT, KAO and NetKAT, and we prove completeness for new variants of KAT: KAT extended with a constant for the full relation, KAT extended with a converse operation, and a version of KAT where the collection of tests only forms a distributive lattice.
With the success of Large Language Models (LLMs), many Generative Vision-Language Models (GVLMs) have been constructed via multimodal instruction tuning. However, the performance of GVLMs in multimodal compositional reasoning remains under-explored. In this paper, we examine both the evaluation metrics (VisualGPTScore, etc.) and current benchmarks for evaluating the compositionality of GVLMs. We identify the syntactical bias in current benchmarks, which is exploited by the linguistic capability of GVLMs. The bias renders VisualGPTScore an insufficient metric for assessing GVLMs. To combat this, we first introduce a SyntaxBias Score, leveraging LLMs to quantify such bias for mitigation. A challenging new task is subsequently added to evaluate the robustness of GVLMs against inherent inclination toward syntactical correctness. Using the bias-mitigated datasets and the new task, we propose a novel benchmark, namely SyntActically DE-biased benchmark (SADE). Our study provides an unbiased benchmark for the compositionality of GVLMs, facilitating future research in this direction (Code and dataset are available at //github.com/TeleeMa/SADE).
Diabetic Retinopathy (DR) stands as the leading cause of blindness globally, particularly affecting individuals between the ages of 20 and 70. This paper presents a Computer-Aided Diagnosis (CAD) system designed for the automatic classification of retinal images into five distinct classes: Normal, Mild, Moderate, Severe, and Proliferative Diabetic Retinopathy (PDR). The proposed system leverages Convolutional Neural Networks (CNNs) employing pre-trained deep learning models. Through the application of fine-tuning techniques, our model is trained on fundus images of diabetic retinopathy with resolutions of 350x350x3 and 224x224x3. Experimental results obtained on the Kaggle platform, utilizing resources comprising 4 CPUs, 17 GB RAM, and 1 GB Disk, demonstrate the efficacy of our approach. The achieved Area Under the Curve (AUC) values for CNN, MobileNet, VGG-16, InceptionV3, and InceptionResNetV2 models are 0.50, 0.70, 0.53, 0.63, and 0.69, respectively.
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