We define extrapolation as any type of statistical inference on a conditional function (e.g., a conditional expectation or conditional quantile) evaluated outside of the support of the conditioning variable. This type of extrapolation occurs in many data analysis applications and can invalidate the resulting conclusions if not taken into account. While extrapolating is straightforward in parametric models, it becomes challenging in nonparametric models. In this work, we extend the nonparametric statistical model to explicitly allow for extrapolation and introduce a class of extrapolation assumptions that can be combined with existing inference techniques to draw extrapolation-aware conclusions. The proposed class of extrapolation assumptions stipulate that the conditional function attains its minimal and maximal directional derivative, in each direction, within the observed support. We illustrate how the framework applies to several statistical applications including prediction and uncertainty quantification. We furthermore propose a consistent estimation procedure that can be used to adjust existing nonparametric estimates to account for extrapolation by providing lower and upper extrapolation bounds. The procedure is empirically evaluated on both simulated and real-world data.
相關內容
Recent studies reveal a significant theoretical link between variational autoencoders (VAEs) and rate-distortion theory, notably in utilizing VAEs to estimate the theoretical upper bound of the information rate-distortion function of images. Such estimated theoretical bounds substantially exceed the performance of existing neural image codecs (NICs). To narrow this gap, we propose a theoretical bound-guided hierarchical VAE (BG-VAE) for NIC. The proposed BG-VAE leverages the theoretical bound to guide the NIC model towards enhanced performance. We implement the BG-VAE using Hierarchical VAEs and demonstrate its effectiveness through extensive experiments. Along with advanced neural network blocks, we provide a versatile, variable-rate NIC that outperforms existing methods when considering both rate-distortion performance and computational complexity. The code is available at BG-VAE.
Nonnegative matrix factorization (NMF) is an effective data representation tool with numerous applications in signal processing and machine learning. However, deploying NMF in a decentralized manner over ad-hoc networks introduces privacy concerns due to the conventional approach of sharing raw data among network agents. To address this, we propose a privacy-preserving algorithm for fully-distributed NMF that decomposes a distributed large data matrix into left and right matrix factors while safeguarding each agent's local data privacy. It facilitates collaborative estimation of the left matrix factor among agents and enables them to estimate their respective right factors without exposing raw data. To ensure data privacy, we secure information exchanges between neighboring agents utilizing the Paillier cryptosystem, a probabilistic asymmetric algorithm for public-key cryptography that allows computations on encrypted data without decryption. Simulation results conducted on synthetic and real-world datasets demonstrate the effectiveness of the proposed algorithm in achieving privacy-preserving distributed NMF over ad-hoc networks.
Despite their unprecedented success, DNNs are notoriously fragile to small shifts in data distribution, demanding effective testing techniques that can assess their dependability. Despite recent advances in DNN testing, there is a lack of systematic testing approaches that assess the DNN's capability to generalise and operate comparably beyond data in their training distribution. We address this gap with DeepKnowledge, a systematic testing methodology for DNN-based systems founded on the theory of knowledge generalisation, which aims to enhance DNN robustness and reduce the residual risk of 'black box' models. Conforming to this theory, DeepKnowledge posits that core computational DNN units, termed Transfer Knowledge neurons, can generalise under domain shift. DeepKnowledge provides an objective confidence measurement on testing activities of DNN given data distribution shifts and uses this information to instrument a generalisation-informed test adequacy criterion to check the transfer knowledge capacity of a test set. Our empirical evaluation of several DNNs, across multiple datasets and state-of-the-art adversarial generation techniques demonstrates the usefulness and effectiveness of DeepKnowledge and its ability to support the engineering of more dependable DNNs. We report improvements of up to 10 percentage points over state-of-the-art coverage criteria for detecting adversarial attacks on several benchmarks, including MNIST, SVHN, and CIFAR.
For doubly-selective channels, delay-Doppler (DD) modulation, mostly known as orthogonal time frequency space (OTFS) modulation, enables simultaneous compensation of delay and Doppler shifts. However, OTFS modulated signal has high peak-to-average power ratio (PAPR) because of its precoding operation performed over the DD domain. In order to deal with this problem, we propose a single-carrier transmission with delay-Doppler domain equalization (SC-DDE). In this system, the discretized time-domain SC signal is converted to the DD domain by discrete Zak transform (DZT) at the receiver side, followed by delay-Doppler domain equalization (DDE). Since equalization is performed in the DD domain, the SC-DDE receiver should acquire the channel delay-Doppler response. To this end, we introduce an embedded pilot-aided channel estimation scheme designed for SC-DDE, which does not affect the peak power property of transmitted signals. Through computer simulation, distribution of PAPR and bit error rate (BER) performance of the proposed system are compared with those of the conventional OTFS and SC with frequency-domain equalization (SC-FDE). As a result, our proposed SC-DDE significantly outperforms SC-FDE in terms of BER at the expense of additional computational complexity at the receiver. Furthermore, SC-DDE shows much lower PAPR than OTFS even though they achieve comparable coded BER performance.
The vector autoregression (VAR) has been widely used in system identification, econometrics, natural science, and many other areas. However, when the state dimension becomes large the parameter dimension explodes. So rank reduced modelling is attractive and is well developed. But a fundamental requirement in almost all applications is stability of the fitted model. And this has not been addressed in the rank reduced case. Here, we develop, for the first time, a closed-form formula for an estimator of a rank reduced transition matrix which is guaranteed to be stable. We show that our estimator is consistent and asymptotically statistically efficient and illustrate it in comparative simulations.
Canonical morphological segmentation is the process of analyzing words into the standard (aka underlying) forms of their constituent morphemes. This is a core task in language documentation, and NLP systems have the potential to dramatically speed up this process. But in typical language documentation settings, training data for canonical morpheme segmentation is scarce, making it difficult to train high quality models. However, translation data is often much more abundant, and, in this work, we present a method that attempts to leverage this data in the canonical segmentation task. We propose a character-level sequence-to-sequence model that incorporates representations of translations obtained from pretrained high-resource monolingual language models as an additional signal. Our model outperforms the baseline in a super-low resource setting but yields mixed results on training splits with more data. While further work is needed to make translations useful in higher-resource settings, our model shows promise in severely resource-constrained settings.
Standard contrastive learning approaches usually require a large number of negatives for effective unsupervised learning and often exhibit slow convergence. We suspect this behavior is due to the suboptimal selection of negatives used for offering contrast to the positives. We counter this difficulty by taking inspiration from support vector machines (SVMs) to present max-margin contrastive learning (MMCL). Our approach selects negatives as the sparse support vectors obtained via a quadratic optimization problem, and contrastiveness is enforced by maximizing the decision margin. As SVM optimization can be computationally demanding, especially in an end-to-end setting, we present simplifications that alleviate the computational burden. We validate our approach on standard vision benchmark datasets, demonstrating better performance in unsupervised representation learning over state-of-the-art, while having better empirical convergence properties.
Recent advances in representation learning have demonstrated an ability to represent information from different modalities such as video, text, and audio in a single high-level embedding vector. In this work we present a self-supervised learning framework that is able to learn a representation that captures finer levels of granularity across different modalities such as concepts or events represented by visual objects or spoken words. Our framework relies on a discretized embedding space created via vector quantization that is shared across different modalities. Beyond the shared embedding space, we propose a Cross-Modal Code Matching objective that forces the representations from different views (modalities) to have a similar distribution over the discrete embedding space such that cross-modal objects/actions localization can be performed without direct supervision. In our experiments we show that the proposed discretized multi-modal fine-grained representation (e.g., pixel/word/frame) can complement high-level summary representations (e.g., video/sentence/waveform) for improved performance on cross-modal retrieval tasks. We also observe that the discretized representation uses individual clusters to represent the same semantic concept across modalities.
The essence of multivariate sequential learning is all about how to extract dependencies in data. These data sets, such as hourly medical records in intensive care units and multi-frequency phonetic time series, often time exhibit not only strong serial dependencies in the individual components (the "marginal" memory) but also non-negligible memories in the cross-sectional dependencies (the "joint" memory). Because of the multivariate complexity in the evolution of the joint distribution that underlies the data generating process, we take a data-driven approach and construct a novel recurrent network architecture, termed Memory-Gated Recurrent Networks (mGRN), with gates explicitly regulating two distinct types of memories: the marginal memory and the joint memory. Through a combination of comprehensive simulation studies and empirical experiments on a range of public datasets, we show that our proposed mGRN architecture consistently outperforms state-of-the-art architectures targeting multivariate time series.
Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191