In this work, we develop a novel efficient quadrature and sparse grid based polynomial interpolation method to price American options with multiple underlying assets. The approach is based on first formulating the pricing of American options using dynamic programming, and then employing static sparse grids to interpolate the continuation value function at each time step. To achieve high efficiency, we first transform the domain from $\mathbb{R}^d$ to $(-1,1)^d$ via a scaled tanh map, and then remove the boundary singularity of the resulting multivariate function over $(-1,1)^d$ by a bubble function and simultaneously, to significantly reduce the number of interpolation points. We rigorously establish that with a proper choice of the bubble function, the resulting function has bounded mixed derivatives up to a certain order, which provides theoretical underpinnings for the use of sparse grids. Numerical experiments for American arithmetic and geometric basket put options with the number of underlying assets up to 16 are presented to validate the effectiveness of the approach.
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ACM SIGACCESS Conference on Computers and Accessibility是為殘疾人和老年人提供與計算機相關的設計、評估、使用和教育研究的首要論壇。我們歡迎提交原始的高質量的有關計算和可訪問性的主題。今年，ASSETS首次將其范圍擴大到包括關于計算機無障礙教育相關主題的原創高質量研究。官網鏈接： ·
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Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states, remains challenging. We propose stabilized neural differential equations (SNDEs), a method to enforce arbitrary manifold constraints for neural differential equations. Our approach is based on a stabilization term that, when added to the original dynamics, renders the constraint manifold provably asymptotically stable. Due to its simplicity, our method is compatible with all common neural differential equation (NDE) models and broadly applicable. In extensive empirical evaluations, we demonstrate that SNDEs outperform existing methods while broadening the types of constraints that can be incorporated into NDE training.
In this paper, we prove the first Bayesian regret bounds for Thompson Sampling in reinforcement learning in a multitude of settings. We simplify the learning problem using a discrete set of surrogate environments, and present a refined analysis of the information ratio using posterior consistency. This leads to an upper bound of order $\widetilde{O}(H\sqrt{d_{l_1}T})$ in the time inhomogeneous reinforcement learning problem where $H$ is the episode length and $d_{l_1}$ is the Kolmogorov $l_1-$dimension of the space of environments. We then find concrete bounds of $d_{l_1}$ in a variety of settings, such as tabular, linear and finite mixtures, and discuss how how our results are either the first of their kind or improve the state-of-the-art.
Neural Model Reprogramming with Similarity Based Mapping for Low-Resource Spoken Command Recognition
In this study, we propose a novel adversarial reprogramming (AR) approach for low-resource spoken command recognition (SCR), and build an AR-SCR system. The AR procedure aims to modify the acoustic signals (from the target domain) to repurpose a pretrained SCR model (from the source domain). To solve the label mismatches between source and target domains, and further improve the stability of AR, we propose a novel similarity-based label mapping technique to align classes. In addition, the transfer learning (TL) technique is combined with the original AR process to improve the model adaptation capability. We evaluate the proposed AR-SCR system on three low-resource SCR datasets, including Arabic, Lithuanian, and dysarthric Mandarin speech. Experimental results show that with a pretrained AM trained on a large-scale English dataset, the proposed AR-SCR system outperforms the current state-of-the-art results on Arabic and Lithuanian speech commands datasets, with only a limited amount of training data.
In this study, we address the interpretability issue in complex, black-box Machine Learning models applied to sequence data. We introduce the Model-Based tree Hidden Semi-Markov Model (MOB-HSMM), an inherently interpretable model aimed at detecting high mortality risk events and discovering hidden patterns associated with the mortality risk in Intensive Care Units (ICU). This model leverages knowledge distilled from Deep Neural Networks (DNN) to enhance predictive performance while offering clear explanations. Our experimental results indicate the improved performance of Model-Based trees (MOB trees) via employing LSTM for learning sequential patterns, which are then transferred to MOB trees. Integrating MOB trees with the Hidden Semi-Markov Model (HSMM) in the MOB-HSMM enables uncovering potential and explainable sequences using available information.
In this work, we aim to characterize the statistical complexity of realizable regression both in the PAC learning setting and the online learning setting. Previous work had established the sufficiency of finiteness of the fat shattering dimension for PAC learnability and the necessity of finiteness of the scaled Natarajan dimension, but little progress had been made towards a more complete characterization since the work of Simon (SICOMP '97). To this end, we first introduce a minimax instance optimal learner for realizable regression and propose a novel dimension that both qualitatively and quantitatively characterizes which classes of real-valued predictors are learnable. We then identify a combinatorial dimension related to the Graph dimension that characterizes ERM learnability in the realizable setting. Finally, we establish a necessary condition for learnability based on a combinatorial dimension related to the DS dimension, and conjecture that it may also be sufficient in this context. Additionally, in the context of online learning we provide a dimension that characterizes the minimax instance optimal cumulative loss up to a constant factor and design an optimal online learner for realizable regression, thus resolving an open question raised by Daskalakis and Golowich in STOC '22.
In this paper, we propose a novel text promptable surgical instrument segmentation approach to overcome challenges associated with diversity and differentiation of surgical instruments in minimally invasive surgeries. We redefine the task as text promptable, thereby enabling a more nuanced comprehension of surgical instruments and adaptability to new instrument types. Inspired by recent advancements in vision-language models, we leverage pretrained image and text encoders as our model backbone and design a text promptable mask decoder consisting of attention- and convolution-based prompting schemes for surgical instrument segmentation prediction. Our model leverages multiple text prompts for each surgical instrument through a new mixture of prompts mechanism, resulting in enhanced segmentation performance. Additionally, we introduce a hard instrument area reinforcement module to improve image feature comprehension and segmentation precision. Extensive experiments on several surgical instrument segmentation datasets demonstrate our model's superior performance and promising generalization capability. To our knowledge, this is the first implementation of a promptable approach to surgical instrument segmentation, offering significant potential for practical application in the field of robotic-assisted surgery.
In this work, we show that a pair of entangled qubits can be used to compute a product privately. More precisely, two participants with a private input from a finite field can perform local operations on a shared, Bell-like quantum state, and when these qubits are later sent to a third participant, the third participant can determine the product of the inputs, but without learning more about the individual inputs. We give a concrete way to realize this product computation for arbitrary finite fields of prime order.
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some sufficient conditions for the stability and convergence of some common multi-step methods, and accordingly, a notion of A-stability for differential equations with memory. Finally, we carry out the computational performance of our theory through numerical examples.
In this paper, we tackle two challenges in multimodal learning for visual recognition: 1) when missing-modality occurs either during training or testing in real-world situations; and 2) when the computation resources are not available to finetune on heavy transformer models. To this end, we propose to utilize prompt learning and mitigate the above two challenges together. Specifically, our modality-missing-aware prompts can be plugged into multimodal transformers to handle general missing-modality cases, while only requiring less than 1% learnable parameters compared to training the entire model. We further explore the effect of different prompt configurations and analyze the robustness to missing modality. Extensive experiments are conducted to show the effectiveness of our prompt learning framework that improves the performance under various missing-modality cases, while alleviating the requirement of heavy model re-training. Code is available.
In this paper, we propose a novel Feature Decomposition and Reconstruction Learning (FDRL) method for effective facial expression recognition. We view the expression information as the combination of the shared information (expression similarities) across different expressions and the unique information (expression-specific variations) for each expression. More specifically, FDRL mainly consists of two crucial networks: a Feature Decomposition Network (FDN) and a Feature Reconstruction Network (FRN). In particular, FDN first decomposes the basic features extracted from a backbone network into a set of facial action-aware latent features to model expression similarities. Then, FRN captures the intra-feature and inter-feature relationships for latent features to characterize expression-specific variations, and reconstructs the expression feature. To this end, two modules including an intra-feature relation modeling module and an inter-feature relation modeling module are developed in FRN. Experimental results on both the in-the-lab databases (including CK+, MMI, and Oulu-CASIA) and the in-the-wild databases (including RAF-DB and SFEW) show that the proposed FDRL method consistently achieves higher recognition accuracy than several state-of-the-art methods. This clearly highlights the benefit of feature decomposition and reconstruction for classifying expressions.
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