The capacity to isolate and recognize individual characters from facsimile images of papyrus manuscripts yields rich opportunities for digital analysis. For this reason the `ICDAR 2023 Competition on Detection and Recognition of Greek Letters on Papyri' was held as part of the 17th International Conference on Document Analysis and Recognition. This paper discusses our submission to the competition. We used an ensemble of YOLOv8 models to detect and classify individual characters and employed two different approaches for refining the character predictions, including a transformer based DeiT approach and a ResNet-50 model trained on a large corpus of unlabelled data using SimCLR, a self-supervised learning method. Our submission won the recognition challenge with a mAP of 42.2%, and was runner-up in the detection challenge with a mean average precision (mAP) of 51.4%. At the more relaxed intersection over union threshold of 0.5, we achieved the highest mean average precision and mean average recall results for both detection and classification. We ran our prediction pipeline on more than 4,500 images from the Oxyrhynchus Papyri to illustrate the utility of our approach, and we release the results publicly in multiple formats.
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Deep learning methods have access to be employed for solving physical systems governed by parametric partial differential equations (PDEs) due to massive scientific data. It has been refined to operator learning that focuses on learning non-linear mapping between infinite-dimensional function spaces, offering interface from observations to solutions. However, state-of-the-art neural operators are limited to constant and uniform discretization, thereby leading to deficiency in generalization on arbitrary discretization schemes for computational domain. In this work, we propose a novel operator learning algorithm, referred to as Dynamic Gaussian Graph Operator (DGGO) that expands neural operators to learning parametric PDEs in arbitrary discrete mechanics problems. The Dynamic Gaussian Graph (DGG) kernel learns to map the observation vectors defined in general Euclidean space to metric vectors defined in high-dimensional uniform metric space. The DGG integral kernel is parameterized by Gaussian kernel weighted Riemann sum approximating and using dynamic message passing graph to depict the interrelation within the integral term. Fourier Neural Operator is selected to localize the metric vectors on spatial and frequency domains. Metric vectors are regarded as located on latent uniform domain, wherein spatial and spectral transformation offer highly regular constraints on solution space. The efficiency and robustness of DGGO are validated by applying it to solve numerical arbitrary discrete mechanics problems in comparison with mainstream neural operators. Ablation experiments are implemented to demonstrate the effectiveness of spatial transformation in the DGG kernel. The proposed method is utilized to forecast stress field of hyper-elastic material with geometrically variable void as engineering application.
Accurate data association is crucial in reducing confusion, such as ID switches and assignment errors, in multi-object tracking (MOT). However, existing advanced methods often overlook the diversity among trajectories and the ambiguity and conflicts present in motion and appearance cues, leading to confusion among detections, trajectories, and associations when performing simple global data association. To address this issue, we propose a simple, versatile, and highly interpretable data association approach called Decomposed Data Association (DDA). DDA decomposes the traditional association problem into multiple sub-problems using a series of non-learning-based modules and selectively addresses the confusion in each sub-problem by incorporating targeted exploitation of new cues. Additionally, we introduce Occlusion-aware Non-Maximum Suppression (ONMS) to retain more occluded detections, thereby increasing opportunities for association with trajectories and indirectly reducing the confusion caused by missed detections. Finally, based on DDA and ONMS, we design a powerful multi-object tracker named DeconfuseTrack, specifically focused on resolving confusion in MOT. Extensive experiments conducted on the MOT17 and MOT20 datasets demonstrate that our proposed DDA and ONMS significantly enhance the performance of several popular trackers. Moreover, DeconfuseTrack achieves state-of-the-art performance on the MOT17 and MOT20 test sets, significantly outperforms the baseline tracker ByteTrack in metrics such as HOTA, IDF1, AssA. This validates that our tracking design effectively reduces confusion caused by simple global association.
The restricted isometry property (RIP) is essential for the linear map to guarantee the successful recovery of low-rank matrices. The existing works show that the linear map generated by the measurement matrices with independent and identically distributed (i.i.d.) entries satisfies RIP with high probability. However, when dealing with non-i.i.d. measurement matrices, such as the rank-one measurements, the RIP compliance may not be guaranteed. In this paper, we show that the RIP can still be achieved with high probability, when the rank-one measurement matrix is constructed by the random unit-modulus vectors. Compared to the existing works, we first address the challenge of establishing RIP for the linear map in non-i.i.d. scenarios. As validated in the experiments, this linear map is memory-efficient, and not only satisfies the RIP but also exhibits similar recovery performance of the low-rank matrices to that of conventional i.i.d. measurement matrices.
Statistical mechanics has made significant contributions to the study of biological neural systems by modeling them as recurrent networks of interconnected units with adjustable interactions. Several algorithms have been proposed to optimize the neural connections to enable network tasks such as information storage (i.e. associative memory) and learning probability distributions from data (i.e. generative modeling). Among these methods, the Unlearning algorithm, aligned with emerging theories of synaptic plasticity, was introduced by John Hopfield and collaborators. The primary objective of this thesis is to understand the effectiveness of Unlearning in both associative memory models and generative models. Initially, we demonstrate that the Unlearning algorithm can be simplified to a linear perceptron model which learns from noisy examples featuring specific internal correlations. The selection of structured training data enables an associative memory model to retrieve concepts as attractors of a neural dynamics with considerable basins of attraction. Subsequently, a novel regularization technique for Boltzmann Machines is presented, proving to outperform previously developed methods in learning hidden probability distributions from data-sets. The Unlearning rule is derived from this new regularized algorithm and is showed to be comparable, in terms of inferential performance, to traditional Boltzmann-Machine learning.
Iterated conditional expectation (ICE) g-computation is an estimation approach for addressing time-varying confounding for both longitudinal and time-to-event data. Unlike other g-computation implementations, ICE avoids the need to specify models for each time-varying covariate. For variance estimation, previous work has suggested the bootstrap. However, bootstrapping can be computationally intense and sensitive to the number of resamples used. Here, we present ICE g-computation as a set of stacked estimating equations. Therefore, the variance for the ICE g-computation estimator can be consistently estimated using the empirical sandwich variance estimator. Performance of the variance estimator was evaluated empirically with a simulation study. The proposed approach is also demonstrated with an illustrative example on the effect of cigarette smoking on the prevalence of hypertension. In the simulation study, the empirical sandwich variance estimator appropriately estimated the variance. When comparing runtimes between the sandwich variance estimator and the bootstrap for the applied example, the sandwich estimator was substantially faster, even when bootstraps were run in parallel. The empirical sandwich variance estimator is a viable option for variance estimation with ICE g-computation.
The consistency of the maximum likelihood estimator for mixtures of elliptically-symmetric distributions for estimating its population version is shown, where the underlying distribution $P$ is nonparametric and does not necessarily belong to the class of mixtures on which the estimator is based. In a situation where $P$ is a mixture of well enough separated but nonparametric distributions it is shown that the components of the population version of the estimator correspond to the well separated components of $P$. This provides some theoretical justification for the use of such estimators for cluster analysis in case that $P$ has well separated subpopulations even if these subpopulations differ from what the mixture model assumes.
Investigation of millimeter (mmWave) and Terahertz (THz) channels relies on channel measurements and estimation of multi-path component (MPC) parameters. As a common measurement technique in the mmWave and THz bands, direction-scan sounding (DSS) resolves angular information and increases the measurable distance. Through mechanical rotation, the DSS creates a virtual multi-antenna sounding system, which however incurs signal phase instability and large data sizes, which are not fully considered in existing estimation algorithms and thus make them ineffective. To tackle this research gap, in this paper, a DSS-oriented space-alternating generalized expectation-maximization (DSS-o-SAGE) algorithm is proposed for channel parameter estimation in mmWave and THz bands. To appropriately capture the measured data in mmWave and THz DSS, the phase instability is modeled by the scanning-direction-dependent signal phases. Furthermore, based on the signal model, the DSS-o-SAGE algorithm is developed, which not only addresses the problems brought by phase instability, but also achieves ultra-low computational complexity by exploiting the narrow antenna beam property of DSS. Simulations in synthetic channels are conducted to demonstrate the efficacy of the proposed algorithm and explore the applicable region of the far-field approximation in DSS-o-SAGE. Last but not least, the proposed DSS-o-SAGE algorithm is applied in real measurements in an indoor corridor scenario at 300~GHz. Compared with results using the baseline noise-elimination method, the channel is characterized more correctly and reasonably based on the DSS-o-SAGE.
Like the notion of computation via (strong) monads serves to classify various flavours of impurity, including exceptions, non-determinism, probability, local and global store, the notion of guardedness classifies well-behavedness of cycles in various settings. In its most general form, the guardedness discipline applies to general symmetric monoidal categories and further specializes to Cartesian and co-Cartesian categories, where it governs guarded recursion and guarded iteration respectively. Here, even more specifically, we deal with the semantics of call-by-value guarded iteration. It was shown by Levy, Power and Thielecke that call-by-value languages can be generally interpreted in Freyd categories, but in order to represent effectful function spaces, such a category must canonically arise from a strong monad. We generalize this fact by showing that representing guarded effectful function spaces calls for certain parametrized monads (in the sense of Uustalu). This provides a description of guardedness as an intrinsic categorical property of programs, complementing the existing description of guardedness as a predicate on a category.
We study the problem of adaptive variable selection in a Gaussian white noise model of intensity $\varepsilon$ under certain sparsity and regularity conditions on an unknown regression function $f$. The $d$-variate regression function $f$ is assumed to be a sum of functions each depending on a smaller number $k$ of variables ($1 \leq k \leq d$). These functions are unknown to us and only few of them are nonzero. We assume that $d=d_\varepsilon \to \infty$ as $\varepsilon \to 0$ and consider the cases when $k$ is fixed and when $k=k_\varepsilon \to \infty$, $k=o(d)$ as $\varepsilon \to 0$. In this work, we introduce an adaptive selection procedure that, under some model assumptions, identifies exactly all nonzero $k$-variate components of $f$. In addition, we establish conditions under which exact identification of the nonzero components is impossible. These conditions ensure that the proposed selection procedure is the best possible in the asymptotically minimax sense with respect to the Hamming risk.
This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of stochastic systems affected by external manipulation (interventions). This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust (out-of-distribution generalizing) prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. Our proposed estimators show, in certain settings, mean squared error improvements compared to both canonical and state-of-the-art estimators. We show that recent research on distributionally robust prediction methods has connections to well-studied estimators from econometrics. This connection leads us to prove that general K-class estimators possess distributional robustness properties. We, furthermore, propose a general framework for distributional robustness with respect to intervention-induced distributions. In this framework, we derive sufficient conditions for the identifiability of distributionally robust prediction methods and present impossibility results that show the necessity of several of these conditions. We present a new structure learning method applicable in additive noise models with directed trees as causal graphs. We prove consistency in a vanishing identifiability setup and provide a method for testing substructure hypotheses with asymptotic family-wise error control that remains valid post-selection. Finally, we present heuristic ideas for learning summary graphs of nonlinear time-series models.
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