In fully Bayesian analyses, prior distributions are specified before observing data. Prior elicitation methods transfigure prior information into quantifiable prior distributions. Recently, methods that leverage copulas have been proposed to accommodate more flexible dependence structures when eliciting multivariate priors. We prove that under broad conditions, the posterior cannot retain many of these flexible prior dependence structures in large-sample settings. We emphasize the impact of this result by overviewing several objectives for prior specification to help practitioners select prior dependence structures that align with their objectives for posterior analysis. Because correctly specifying the dependence structure a priori can be difficult, we consider how the choice of prior copula impacts the posterior distribution in terms of asymptotic convergence of the posterior mode. Our resulting recommendations streamline the prior elicitation process.
相關內容
We propose a modified density estimation problem that is highly effective for detecting anomalies in tabular data. Our approach assumes that the density function is relatively stable (with lower variance) around normal samples. We have verified this hypothesis empirically using a wide range of real-world data. Then, we present a variance-stabilized density estimation problem for maximizing the likelihood of the observed samples while minimizing the variance of the density around normal samples. To obtain a reliable anomaly detector, we introduce a spectral ensemble of autoregressive models for learning the variance-stabilized distribution. We have conducted an extensive benchmark with 52 datasets, demonstrating that our method leads to state-of-the-art results while alleviating the need for data-specific hyperparameter tuning. Finally, we have used an ablation study to demonstrate the importance of each of the proposed components, followed by a stability analysis evaluating the robustness of our model.
In Gaussian graphical model selection, noise-corrupted samples present significant challenges. It is known that even minimal amounts of noise can obscure the underlying structure, leading to fundamental identifiability issues. A recent line of work addressing this "robust model selection" problem narrows its focus to tree-structured graphical models. Even within this specific class of models, exact structure recovery is shown to be impossible. However, several algorithms have been developed that are known to provably recover the underlying tree-structure up to an (unavoidable) equivalence class. In this paper, we extend these results beyond tree-structured graphs. We first characterize the equivalence class up to which general graphs can be recovered in the presence of noise. Despite the inherent ambiguity (which we prove is unavoidable), the structure that can be recovered reveals local clustering information and global connectivity patterns in the underlying model. Such information is useful in a range of real-world problems, including power grids, social networks, protein-protein interactions, and neural structures. We then propose an algorithm which provably recovers the underlying graph up to the identified ambiguity. We further provide finite sample guarantees in the high-dimensional regime for our algorithm and validate our results through numerical simulations.
We propose a new Bayesian heteroskedastic Markov-switching structural vector autoregression with data-driven time-varying identification. The model selects alternative exclusion restrictions over time and, as a condition for the search, allows to verify identification through heteroskedasticity within each regime. Based on four alternative monetary policy rules, we show that a monthly six-variable system supports time variation in US monetary policy shock identification. In the sample-dominating first regime, systematic monetary policy follows a Taylor rule extended by the term spread, effectively curbing inflation. In the second regime, occurring after 2000 and gaining more persistence after the global financial and COVID crises, it is characterized by a money-augmented Taylor rule. This regime's unconventional monetary policy provides economic stimulus, features the liquidity effect, and is complemented by a pure term spread shock. Absent the specific monetary policy of the second regime, inflation would be over one percentage point higher on average after 2008.
Learned indexes leverage machine learning models to accelerate query answering in databases, showing impressive practical performance. However, theoretical understanding of these methods remains incomplete. Existing research suggests that learned indexes have superior asymptotic complexity compared to their non-learned counterparts, but these findings have been established under restrictive probabilistic assumptions. Specifically, for a sorted array with $n$ elements, it has been shown that learned indexes can find a key in $O(\log(\log n))$ expected time using at most linear space, compared with $O(\log n)$ for non-learned methods. In this work, we prove $O(1)$ expected time can be achieved with at most linear space, thereby establishing the tightest upper bound so far for the time complexity of an asymptotically optimal learned index. Notably, we use weaker probabilistic assumptions than prior work, meaning our results generalize previous efforts. Furthermore, we introduce a new measure of statistical complexity for data. This metric exhibits an information-theoretical interpretation and can be estimated in practice. This characterization provides further theoretical understanding of learned indexes, by helping to explain why some datasets seem to be particularly challenging for these methods.
By concatenating a polar transform with a convolutional transform, polarization-adjusted convolutional (PAC) codes can reach the dispersion approximation bound in certain rate cases. However, the sequential decoding nature of traditional PAC decoding algorithms results in high decoding latency. Due to the parallel computing capability, deep neural network (DNN) decoders have emerged as a promising solution. In this paper, we propose three types of DNN decoders for PAC codes: multi-layer perceptron (MLP), convolutional neural network (CNN), and recurrent neural network (RNN). The performance of these DNN decoders is evaluated through extensive simulation. Numerical results show that the MLP decoder has the best error-correction performance under a similar model parameter number.
Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.
Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.
We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.
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