A new generalization of Reed-Solomon codes is given. This new generalization has similar information rate bound and similar distance rate bound as BCH codes. It also approaches to the Gilbert bound as Goppa codes. Nevertheless, decoding these new codes is much faster than decoding BCH codes.
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Discovering causal relationships from observational data is a fundamental yet challenging task. Invariant causal prediction (ICP, Peters et al., 2016) is a method for causal feature selection which requires data from heterogeneous settings and exploits that causal models are invariant. ICP has been extended to general additive noise models and to nonparametric settings using conditional independence tests. However, the latter often suffer from low power (or poor type I error control) and additive noise models are not suitable for applications in which the response is not measured on a continuous scale, but reflects categories or counts. Here, we develop transformation-model (TRAM) based ICP, allowing for continuous, categorical, count-type, and uninformatively censored responses (these model classes, generally, do not allow for identifiability when there is no exogenous heterogeneity). As an invariance test, we propose TRAM-GCM based on the expected conditional covariance between environments and score residuals with uniform asymptotic level guarantees. For the special case of linear shift TRAMs, we also consider TRAM-Wald, which tests invariance based on the Wald statistic. We provide an open-source R package 'tramicp' and evaluate our approach on simulated data and in a case study investigating causal features of survival in critically ill patients.
We aim to solve the problem of data-driven collision-distance estimation given 3-dimensional (3D) geometries. Conventional algorithms suffer from low accuracy due to their reliance on limited representations, such as point clouds. In contrast, our previous graph-based model, GraphDistNet, achieves high accuracy using edge information but incurs higher message-passing costs with growing graph size, limiting its applicability to 3D geometries. To overcome these challenges, we propose GDN-R, a novel 3D graph-based estimation network.GDN-R employs a layer-wise probabilistic graph-rewiring algorithm leveraging the differentiable Gumbel-top-K relaxation. Our method accurately infers minimum distances through iterative graph rewiring and updating relevant embeddings. The probabilistic rewiring enables fast and robust embedding with respect to unforeseen categories of geometries. Through 41,412 random benchmark tasks with 150 pairs of 3D objects, we show GDN-R outperforms state-of-the-art baseline methods in terms of accuracy and generalizability. We also show that the proposed rewiring improves the update performance reducing the size of the estimation model. We finally show its batch prediction and auto-differentiation capabilities for trajectory optimization in both simulated and real-world scenarios.
This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise stationary spatio-temporal process, we consider simultaneous estimation of the number and locations of change-points, and model parameters in each segment. A composite likelihood-based criterion is developed for change-point and parameters estimation. Under the framework of increasing domain asymptotics, theoretical results including consistency and distribution of the estimators are derived under mild conditions. In contrast to classical results in fixed dimensional time series that the localization error of change-point estimator is $O_{p}(1)$, exact recovery of true change-points can be achieved in the spatio-temporal setting. More surprisingly, the consistency of change-point estimation can be achieved without any penalty term in the criterion function. In addition, we further establish consistency of the number and locations of the change-point estimator under the infill asymptotics framework where the time domain is increasing while the spatial sampling domain is fixed. A computationally efficient pruned dynamic programming algorithm is developed for the challenging criterion optimization problem. Extensive simulation studies and an application to U.S. precipitation data are provided to demonstrate the effectiveness and practicality of the proposed method.
We consider Gibbs distributions, which are families of probability distributions over a discrete space $\Omega$ with probability mass function of the form $\mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)}$ for $\beta$ in an interval $[\beta_{\min}, \beta_{\max}]$ and $H( \omega ) \in \{0 \} \cup [1, n]$. The partition function is the normalization factor $Z(\beta)=\sum_{\omega \in\Omega}e^{\beta H(\omega)}$. Two important parameters of these distributions are the log partition ratio $q = \log \tfrac{Z(\beta_{\max})}{Z(\beta_{\min})}$ and the counts $c_x = |H^{-1}(x)|$. These are correlated with system parameters in a number of physical applications and sampling algorithms. Our first main result is to estimate the counts $c_x$ using roughly $\tilde O( \frac{q}{\varepsilon^2})$ samples for general Gibbs distributions and $\tilde O( \frac{n^2}{\varepsilon^2} )$ samples for integer-valued distributions (ignoring some second-order terms and parameters), and we show this is optimal up to logarithmic factors. We illustrate with improved algorithms for counting connected subgraphs, independent sets, and perfect matchings. As a key subroutine, we also develop algorithms to compute the partition function $Z$ using $\tilde O(\frac{q}{\varepsilon^2})$ samples for general Gibbs distributions and using $\tilde O(\frac{n^2}{\varepsilon^2})$ samples for integer-valued distributions.
Simulation-based inference (SBI) methods such as approximate Bayesian computation (ABC), synthetic likelihood, and neural posterior estimation (NPE) rely on simulating statistics to infer parameters of intractable likelihood models. However, such methods are known to yield untrustworthy and misleading inference outcomes under model misspecification, thus hindering their widespread applicability. In this work, we propose the first general approach to handle model misspecification that works across different classes of SBI methods. Leveraging the fact that the choice of statistics determines the degree of misspecification in SBI, we introduce a regularized loss function that penalises those statistics that increase the mismatch between the data and the model. Taking NPE and ABC as use cases, we demonstrate the superior performance of our method on high-dimensional time-series models that are artificially misspecified. We also apply our method to real data from the field of radio propagation where the model is known to be misspecified. We show empirically that the method yields robust inference in misspecified scenarios, whilst still being accurate when the model is well-specified.
Preserving individual privacy while enabling collaborative data sharing is crucial for organizations. Synthetic data generation is one solution, producing artificial data that mirrors the statistical properties of private data. While numerous techniques have been devised under differential privacy, they predominantly assume data is centralized. However, data is often distributed across multiple clients in a federated manner. In this work, we initiate the study of federated synthetic tabular data generation. Building upon a SOTA central method known as AIM, we present DistAIM and FLAIM. We show it is straightforward to distribute AIM, extending a recent approach based on secure multi-party computation which necessitates additional overhead, making it less suited to federated scenarios. We then demonstrate that naively federating AIM can lead to substantial degradation in utility under the presence of heterogeneity. To mitigate both issues, we propose an augmented FLAIM approach that maintains a private proxy of heterogeneity. We simulate our methods across a range of benchmark datasets under different degrees of heterogeneity and show this can improve utility while reducing overhead.
The video-language (VL) pretraining has achieved remarkable improvement in multiple downstream tasks. However, the current VL pretraining framework is hard to extend to multiple modalities (N modalities, N>=3) beyond vision and language. We thus propose LanguageBind, taking the language as the bind across different modalities because the language modality is well-explored and contains rich semantics. Specifically, we freeze the language encoder acquired by VL pretraining, then train encoders for other modalities with contrastive learning. As a result, all modalities are mapped to a shared feature space, implementing multi-modal semantic alignment. While LanguageBind ensures that we can extend VL modalities to N modalities, we also need a high-quality dataset with alignment data pairs centered on language. We thus propose VIDAL-10M with Video, Infrared, Depth, Audio and their corresponding Language, naming as VIDAL-10M. In our VIDAL-10M, all videos are from short video platforms with complete semantics rather than truncated segments from long videos, and all the video, depth, infrared, and audio modalities are aligned to their textual descriptions. After pretraining on VIDAL-10M, we outperform ImageBind by 1.2% R@1 on the MSR-VTT dataset with only 15% of the parameters in the zero-shot video-text retrieval, validating the high quality of our dataset. Beyond this, our LanguageBind has achieved great improvement in the zero-shot video, audio, depth, and infrared understanding tasks. For instance, on the LLVIP and NYU-D datasets, LanguageBind outperforms ImageBind-huge with 23.8% and 11.1% top-1 accuracy. Code address: //github.com/PKU-YuanGroup/LanguageBind.
Recently, Sato et al. proposed an public verifiable blind quantum computation (BQC) protocol by inserting a third-party arbiter. However, it is not true public verifiable in a sense, because the arbiter is determined in advance and participates in the whole process. In this paper, a public verifiable protocol for measurement-only BQC is proposed. The fidelity between arbitrary states and the graph states of 2-colorable graphs is estimated by measuring the entanglement witnesses of the graph states,so as to verify the correctness of the prepared graph states. Compared with the previous protocol, our protocol is public verifiable in the true sense by allowing other random clients to execute the public verification. It also has greater advantages in the efficiency, where the number of local measurements is O(n^3*log {n}) and graph states' copies is O(n^2*log{n}).
We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.
Recommender systems are widely used in big information-based companies such as Google, Twitter, LinkedIn, and Netflix. A recommender system deals with the problem of information overload by filtering important information fragments according to users' preferences. In light of the increasing success of deep learning, recent studies have proved the benefits of using deep learning in various recommendation tasks. However, most proposed techniques only aim to target individuals, which cannot be efficiently applied in group recommendation. In this paper, we propose a deep learning architecture to solve the group recommendation problem. On the one hand, as different individual preferences in a group necessitate preference trade-offs in making group recommendations, it is essential that the recommendation model can discover substitutes among user behaviors. On the other hand, it has been observed that a user as an individual and as a group member behaves differently. To tackle such problems, we propose using an attention mechanism to capture the impact of each user in a group. Specifically, our model automatically learns the influence weight of each user in a group and recommends items to the group based on its members' weighted preferences. We conduct extensive experiments on four datasets. Our model significantly outperforms baseline methods and shows promising results in applying deep learning to the group recommendation problem.
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