The Na\"ive Bayes has proven to be a tractable and efficient method for classification in multivariate analysis. However, features are usually correlated, a fact that violates the Na\"ive Bayes' assumption of conditional independence, and may deteriorate the method's performance. Moreover, datasets are often characterized by a large number of features, which may complicate the interpretation of the results as well as slow down the method's execution. In this paper we propose a sparse version of the Na\"ive Bayes classifier that is characterized by three properties. First, the sparsity is achieved taking into account the correlation structure of the covariates. Second, different performance measures can be used to guide the selection of features. Third, performance constraints on groups of higher interest can be included. Our proposal leads to a smart search, which yields competitive running times, whereas the flexibility in terms of performance measure for classification is integrated. Our findings show that, when compared against well-referenced feature selection approaches, the proposed sparse Na\"ive Bayes obtains competitive results regarding accuracy, sparsity and running times for balanced datasets. In the case of datasets with unbalanced (or with different importance) classes, a better compromise between classification rates for the different classes is achieved.
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Large Language Models (LLMs), benefiting from the auto-regressive modelling approach performed on massive unannotated texts corpora, demonstrates powerful perceptual and reasoning capabilities. However, as for extending auto-regressive modelling to multi-modal scenarios to build Large Multi-modal Models (LMMs), there lies a great difficulty that the image information is processed in the LMM as continuous visual embeddings, which cannot obtain discrete supervised labels for classification. In this paper, we successfully perform multi-modal auto-regressive modeling with a unified objective for the first time. Specifically, we propose the concept of visual words, which maps the visual features to probability distributions over LLM's vocabulary, providing supervision information for visual modelling. We further explore the distribution of visual features in the semantic space within LMM and the possibility of using text embeddings to represent visual information. Experimental results and ablation studies on 5 VQA tasks and 4 benchmark toolkits validate the powerful performance of our proposed approach.
We present ReCAT, a recursive composition augmented Transformer that is able to explicitly model hierarchical syntactic structures of raw texts without relying on gold trees during both learning and inference. Existing research along this line restricts data to follow a hierarchical tree structure and thus lacks inter-span communications. To overcome the problem, we propose a novel contextual inside-outside (CIO) layer that learns contextualized representations of spans through bottom-up and top-down passes, where a bottom-up pass forms representations of high-level spans by composing low-level spans, while a top-down pass combines information inside and outside a span. By stacking several CIO layers between the embedding layer and the attention layers in Transformer, the ReCAT model can perform both deep intra-span and deep inter-span interactions, and thus generate multi-grained representations fully contextualized with other spans. Moreover, the CIO layers can be jointly pre-trained with Transformers, making ReCAT enjoy scaling ability, strong performance, and interpretability at the same time. We conduct experiments on various sentence-level and span-level tasks. Evaluation results indicate that ReCAT can significantly outperform vanilla Transformer models on all span-level tasks and baselines that combine recursive networks with Transformers on natural language inference tasks. More interestingly, the hierarchical structures induced by ReCAT exhibit strong consistency with human-annotated syntactic trees, indicating good interpretability brought by the CIO layers.
The Bell regression model (BRM) is a statistical model that is often used in the analysis of count data that exhibits overdispersion. In this study, we propose a Bayesian analysis of the BRM and offer a new perspective on its application. Specifically, we introduce a G-prior distribution for Bayesian inference in BRM, in addition to a flat-normal prior distribution. To compare the performance of the proposed prior distributions, we conduct a simulation study and demonstrate that the G-prior distribution provides superior estimation results for the BRM. Furthermore, we apply the methodology to real data and compare the BRM to the Poisson regression model using various model selection criteria. Our results provide valuable insights into the use of Bayesian methods for estimation and inference of the BRM and highlight the importance of considering the choice of prior distribution in the analysis of count data.
Kr\"oncke has shown that the Fubini-Study metric is an unstable generalized stationary solution of Ricci flow [Kr\"o20]. In this paper, we carry out numerical simulations which indicate that Ricci flow solutions originating at unstable perturbations of the Fubini-Study metric develop local singularities modeled by the blowdown soliton discovered in [FIK03].
Unfolding can tackle the path-explosion problem caused by concurrency. Traditional unfolding generation faces an NP-complete problem when adding events to the unfolding structure, which also exists in the case of verifying linear temporal logic (LTL). The reason is that it is necessary to enumerate possible concurrent event combinations after adding an event. Many state-of-the-art methods optimally explore unfolding-based structure (called event structure) by a tree-like structure, which should be constructed on the event structure with complete conflict and causal relations. However, a synchronization of a Petri net and the Buchi representation of LTL as a folded net can not represent complete conflict and causal relations. Thus, it is difficult to apply such a tree-like structure directly on the folded net. To resolve this difficulty, we propose a new method, called partial-order checking with unfolding, to verify LTL based on PDNet (program dependence net). We define an exploration tree with a new notion of delayed transitions, which is different from the existing tree-like structure. It improves the unfolding generation by avoiding all possible event combinations. Then, we propose an algorithm to simultaneously construct the exploration tree while generating the unfolding structure, as well as checking LTL. We implement a tool PUPER for concurrent programs with POSIX threads. It improves traditional unfolding generations via our exploration tree-based algorithms and shows better performance than SPIN and DiVine on the used benchmarks.
We study a generalization of the well-known disjoint paths problem which we call the metric Menger problem, denoted MM(r,k), where one is given two subsets of a graph and must decide whether they can be connected by $k$ paths of pairwise distance at least $r$. We prove that this problem is NP-complete for every $r\geq 3$ and $k\geq 2$ by giving a reduction from 3SAT. This resolves a conjecture recently stated by Georgakopoulos and Papasoglu. On the other hand, we show that the problem is in XP when parameterised by treewidth and maximum degree by observing that it is `locally checkable'. In the case $r\leq 3$, we prove that it suffices to parameterise by treewidth. We also state some open questions relating to this work.
To date, most methods for simulating conditioned diffusions are limited to the Euclidean setting. The conditioned process can be constructed using a change of measure known as Doob's $h$-transform. The specific type of conditioning depends on a function $h$ which is typically unknown in closed form. To resolve this, we extend the notion of guided processes to a manifold $M$, where one replaces $h$ by a function based on the heat kernel on $M$. We consider the case of a Brownian motion with drift, constructed using the frame bundle of $M$, conditioned to hit a point $x_T$ at time $T$. We prove equivalence of the laws of the conditioned process and the guided process with a tractable Radon-Nikodym derivative. Subsequently, we show how one can obtain guided processes on any manifold $N$ that is diffeomorphic to $M$ without assuming knowledge of the heat kernel on $N$. We illustrate our results with numerical simulations and an example of parameter estimation where a diffusion process on the torus is observed discretely in time.
We present a simple self-training method that achieves 87.4% top-1 accuracy on ImageNet, which is 1.0% better than the state-of-the-art model that requires 3.5B weakly labeled Instagram images. On robustness test sets, it improves ImageNet-A top-1 accuracy from 16.6% to 74.2%, reduces ImageNet-C mean corruption error from 45.7 to 31.2, and reduces ImageNet-P mean flip rate from 27.8 to 16.1. To achieve this result, we first train an EfficientNet model on labeled ImageNet images and use it as a teacher to generate pseudo labels on 300M unlabeled images. We then train a larger EfficientNet as a student model on the combination of labeled and pseudo labeled images. We iterate this process by putting back the student as the teacher. During the generation of the pseudo labels, the teacher is not noised so that the pseudo labels are as good as possible. But during the learning of the student, we inject noise such as data augmentation, dropout, stochastic depth to the student so that the noised student is forced to learn harder from the pseudo labels.
Recently, ensemble has been applied to deep metric learning to yield state-of-the-art results. Deep metric learning aims to learn deep neural networks for feature embeddings, distances of which satisfy given constraint. In deep metric learning, ensemble takes average of distances learned by multiple learners. As one important aspect of ensemble, the learners should be diverse in their feature embeddings. To this end, we propose an attention-based ensemble, which uses multiple attention masks, so that each learner can attend to different parts of the object. We also propose a divergence loss, which encourages diversity among the learners. The proposed method is applied to the standard benchmarks of deep metric learning and experimental results show that it outperforms the state-of-the-art methods by a significant margin on image retrieval tasks.
Automatic License Plate Recognition (ALPR) has been a frequent topic of research due to many practical applications. However, many of the current solutions are still not robust in real-world situations, commonly depending on many constraints. This paper presents a robust and efficient ALPR system based on the state-of-the-art YOLO object detection. The Convolutional Neural Networks (CNNs) are trained and fine-tuned for each ALPR stage so that they are robust under different conditions (e.g., variations in camera, lighting, and background). Specially for character segmentation and recognition, we design a two-stage approach employing simple data augmentation tricks such as inverted License Plates (LPs) and flipped characters. The resulting ALPR approach achieved impressive results in two datasets. First, in the SSIG dataset, composed of 2,000 frames from 101 vehicle videos, our system achieved a recognition rate of 93.53% and 47 Frames Per Second (FPS), performing better than both Sighthound and OpenALPR commercial systems (89.80% and 93.03%, respectively) and considerably outperforming previous results (81.80%). Second, targeting a more realistic scenario, we introduce a larger public dataset, called UFPR-ALPR dataset, designed to ALPR. This dataset contains 150 videos and 4,500 frames captured when both camera and vehicles are moving and also contains different types of vehicles (cars, motorcycles, buses and trucks). In our proposed dataset, the trial versions of commercial systems achieved recognition rates below 70%. On the other hand, our system performed better, with recognition rate of 78.33% and 35 FPS.
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