The analysis of animal movement has gained attention recently. New continuous-time models and statistical methods have been developed to estimate some sets related to their movements, such as the home-range and the core-area among others, when the information of the trajectory is provided by a GPS. Because data transfer costs and GPS battery life are practical constraints in ecological studies, the experimental designer must make critical sampling decisions in order to maximize information. To capture fine-scale motion, long-term behavior must be sacrificed, and vice versa. To overcome this limitation, we introduce the on--off sampling scheme, where the GPS is alternately on and off. This scheme is already used in practice but with insufficient statistical theoretical support. We prove the consistency of home-range estimators with an underlying reflected diffusion model under this sampling method (in terms of the Hausdorff distance). The same rate of convergence is achieved as in the case where the GPS is always on for the whole experiment. This is illustrated by a simulation study and real data. We also provide estimators of the stationary distribution, its level sets (which give estimators of the core area), and the drift function.
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Measuring the semantic similarity between two sentences is still an important task. The word mover's distance (WMD) computes the similarity via the optimal alignment between the sets of word embeddings. However, WMD does not utilize word order, making it challenging to distinguish sentences with significant overlaps of similar words, even if they are semantically very different. Here, we attempt to improve WMD by incorporating the sentence structure represented by BERT's self-attention matrix (SAM). The proposed method is based on the Fused Gromov-Wasserstein distance, which simultaneously considers the similarity of the word embedding and the SAM for calculating the optimal transport between two sentences. Experiments demonstrate the proposed method enhances WMD and its variants in paraphrase identification with near-equivalent performance in semantic textual similarity. Our code is available at \url{//github.com/ymgw55/WSMD}.
Data is a cornerstone for fine-tuning large language models, yet acquiring suitable data remains challenging. Challenges encompassed data scarcity, linguistic diversity, and domain-specific content. This paper presents lessons learned while crawling and refining data tailored for fine-tuning Vietnamese language models. Crafting such a dataset, while accounting for linguistic intricacies and striking a balance between inclusivity and accuracy, demands meticulous planning. Our paper presents a multidimensional strategy including leveraging existing datasets in the English language and developing customized data-crawling scripts with the assistance of generative AI tools. A fine-tuned LLM model for the Vietnamese language, which was produced using resultant datasets, demonstrated good performance while generating Vietnamese news articles from prompts. The study offers practical solutions and guidance for future fine-tuning models in languages like Vietnamese.
Speaker localization for binaural microphone arrays has been widely studied for applications such as speech communication, video conferencing, and robot audition. Many methods developed for this task, including the direct path dominance (DPD) test, share common stages in their processing, which include transformation using the short-time Fourier transform (STFT), and a direction of arrival (DOA) search that is based on the head related transfer function (HRTF) set. In this paper, alternatives to these processing stages, motivated by human hearing, are proposed. These include incorporating an auditory filter bank to replace the STFT, and a new DOA search based on transformed HRTF as steering vectors. A simulation study and an experimental study are conducted to validate the proposed alternatives, and both are applied to two binaural DOA estimation methods; the results show that the proposed method compares favorably with current methods.
Motivated by models of human decision making proposed to explain commonly observed deviations from conventional expected value preferences, we formulate two stochastic multi-armed bandit problems with distorted probabilities on the reward distributions: the classic $K$-armed bandit and the linearly parameterized bandit settings. We consider the aforementioned problems in the regret minimization as well as best arm identification framework for multi-armed bandits. For the regret minimization setting in $K$-armed as well as linear bandit problems, we propose algorithms that are inspired by Upper Confidence Bound (UCB) algorithms, incorporate reward distortions, and exhibit sublinear regret. For the $K$-armed bandit setting, we derive an upper bound on the expected regret for our proposed algorithm, and then we prove a matching lower bound to establish the order-optimality of our algorithm. For the linearly parameterized setting, our algorithm achieves a regret upper bound that is of the same order as that of regular linear bandit algorithm called Optimism in the Face of Uncertainty Linear (OFUL) bandit algorithm, and unlike OFUL, our algorithm handles distortions and an arm-dependent noise model. For the best arm identification problem in the $K$-armed bandit setting, we propose algorithms, derive guarantees on their performance, and also show that these algorithms are order optimal by proving matching fundamental limits on performance. For best arm identification in linear bandits, we propose an algorithm and establish sample complexity guarantees. Finally, we present simulation experiments which demonstrate the advantages resulting from using distortion-aware learning algorithms in a vehicular traffic routing application.
Question answering methods are well-known for leveraging data bias, such as the language prior in visual question answering and the position bias in machine reading comprehension (extractive question answering). Current debiasing methods often come at the cost of significant in-distribution performance to achieve favorable out-of-distribution generalizability, while non-debiasing methods sacrifice a considerable amount of out-of-distribution performance in order to obtain high in-distribution performance. Therefore, it is challenging for them to deal with the complicated changing real-world situations. In this paper, we propose a simple yet effective novel loss function with adaptive loose optimization, which seeks to make the best of both worlds for question answering. Our main technical contribution is to reduce the loss adaptively according to the ratio between the previous and current optimization state on mini-batch training data. This loose optimization can be used to prevent non-debiasing methods from overlearning data bias while enabling debiasing methods to maintain slight bias learning. Experiments on the visual question answering datasets, including VQA v2, VQA-CP v1, VQA-CP v2, GQA-OOD, and the extractive question answering dataset SQuAD demonstrate that our approach enables QA methods to obtain state-of-the-art in- and out-of-distribution performance in most cases. The source code has been released publicly in \url{//github.com/reml-group/ALO}.
We propose models and algorithms for learning about random directions in simplex-valued data. The models are applied to the study of income level proportions and their changes over time in a geostatistical area. There are several notable challenges in the analysis of simplex-valued data: the measurements must respect the simplex constraint and the changes exhibit spatiotemporal smoothness and may be heterogeneous. To that end, we propose Bayesian models that draw from and expand upon building blocks in circular and spatial statistics by exploiting a suitable transformation for the simplex-valued data. Our models also account for spatial correlation across locations in the simplex and the heterogeneous patterns via mixture modeling. We describe some properties of the models and model fitting via MCMC techniques. Our models and methods are applied to an analysis of movements and trends of income categories using the Home Mortgage Disclosure Act data.
Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws. The family of minmod limiters serves as the prototype example. Here, we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et. al. 1982. The van Albada (vA) limiter is smoother near extrema, and consequently, in many cases, it outperforms the results obtained using the standard minmod limiter. In particular, we prove that the vA limiter ensures 1D TVD stability and demonstrate that it yields noticeable improvement in computation of one- and two-dimensional systems.
This contribution introduces a model order reduction approach for an advection-reaction problem with a parametrized reaction function. The underlying discretization uses an ultraweak formulation with an $L^2$-like trial space and an 'optimal' test space as introduced by Demkowicz et al. This ensures the stability of the discretization and in addition allows for a symmetric reformulation of the problem in terms of a dual solution which can also be interpreted as the normal equations of an adjoint least-squares problem. Classic model order reduction techniques can then be applied to the space of dual solutions which also immediately gives a reduced primal space. We show that the necessary computations do not require the reconstruction of any primal solutions and can instead be performed entirely on the space of dual solutions. We prove exponential convergence of the Kolmogorov $N$-width and show that a greedy algorithm produces quasi-optimal approximation spaces for both the primal and the dual solution space. Numerical experiments based on the benchmark problem of a catalytic filter confirm the applicability of the proposed method.
The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree decomposition of the computational domain is deployed and each cubic cell is treated as an SBFEM subdomain. The surfaces of each subdomain are discretized in the finite element sense. We improve on this idea by combining the semi-analytical concept of the SBFEM with certain transition elements on the subdomains' surfaces. Thus, we avoid the triangulation of surfaces employed in previous works and consequently reduce the number of surface elements and degrees of freedom. In addition, these discretizations allow coupling elements of arbitrary order such that local p-refinement can be achieved straightforwardly.
Log-concave sampling has witnessed remarkable algorithmic advances in recent years, but the corresponding problem of proving lower bounds for this task has remained elusive, with lower bounds previously known only in dimension one. In this work, we establish the following query lower bounds: (1) sampling from strongly log-concave and log-smooth distributions in dimension $d\ge 2$ requires $\Omega(\log \kappa)$ queries, which is sharp in any constant dimension, and (2) sampling from Gaussians in dimension $d$ (hence also from general log-concave and log-smooth distributions in dimension $d$) requires $\widetilde \Omega(\min(\sqrt\kappa \log d, d))$ queries, which is nearly sharp for the class of Gaussians. Here $\kappa$ denotes the condition number of the target distribution. Our proofs rely upon (1) a multiscale construction inspired by work on the Kakeya conjecture in geometric measure theory, and (2) a novel reduction that demonstrates that block Krylov algorithms are optimal for this problem, as well as connections to lower bound techniques based on Wishart matrices developed in the matrix-vector query literature.
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