Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with efficient computation and fast convergence to the nominal level. Specifically, we propose to use a small number of independent multi-runs to acquire distribution information and construct a t-based confidence interval. Our method requires minimal additional computation and memory beyond the standard updating of estimates, making the inference process almost cost-free. We provide a rigorous theoretical guarantee for the confidence interval, demonstrating that the coverage is approximately exact with an explicit convergence rate and allowing for high confidence level inference. In particular, a new Gaussian approximation result is developed for the online estimators to characterize the coverage properties of our confidence intervals in terms of relative errors. Additionally, our method also allows for leveraging parallel computing to further accelerate calculations using multiple cores. It is easy to implement and can be integrated with existing stochastic algorithms without the need for complicated modifications.
相關內容
The human cognitive system exhibits remarkable flexibility and generalization capabilities, partly due to its ability to form low-dimensional, compositional representations of the environment. In contrast, standard neural network architectures often struggle with abstract reasoning tasks, overfitting, and requiring extensive data for training. This paper investigates the impact of the relational bottleneck -- a mechanism that focuses processing on relations among inputs -- on the learning of factorized representations conducive to compositional coding and the attendant flexibility of processing. We demonstrate that such a bottleneck not only improves generalization and learning efficiency, but also aligns network performance with human-like behavioral biases. Networks trained with the relational bottleneck developed orthogonal representations of feature dimensions latent in the dataset, reflecting the factorized structure thought to underlie human cognitive flexibility. Moreover, the relational network mimics human biases towards regularity without pre-specified symbolic primitives, suggesting that the bottleneck fosters the emergence of abstract representations that confer flexibility akin to symbols.
We give extensive empirical evidence against the common belief that variational learning is ineffective for large neural networks. We show that an optimizer called Improved Variational Online Newton (IVON) consistently matches or outperforms Adam for training large networks such as GPT-2 and ResNets from scratch. IVON's computational costs are nearly identical to Adam but its predictive uncertainty is better. We show several new use cases of IVON where we improve fine-tuning and model merging in Large Language Models, accurately predict generalization error, and faithfully estimate sensitivity to data. We find overwhelming evidence in support of effectiveness of variational learning.
Bayesian optimization is a popular framework for efficiently finding high-quality solutions to difficult problems based on limited prior information. As a rule, these algorithms operate by iteratively choosing what to try next until some predefined budget has been exhausted. We investigate replacing this de facto stopping rule with an $(\epsilon, \delta)$-criterion: stop when a solution has been found whose value is within $\epsilon > 0$ of the optimum with probability at least $1 - \delta$ under the model. Given access to the prior distribution of problems, we show how to verify this condition in practice using a limited number of draws from the posterior. For Gaussian process priors, we prove that Bayesian optimization with the proposed criterion stops in finite time and returns a point that satisfies the $(\epsilon, \delta)$-criterion under mild assumptions. These findings are accompanied by extensive empirical results which demonstrate the strengths and weaknesses of this approach.
Significantly simplifying the creation of optimization models for real-world business problems has long been a major goal in applying mathematical optimization more widely to important business and societal decisions. The recent capabilities of Large Language Models (LLMs) present a timely opportunity to achieve this goal. Therefore, we propose research at the intersection of LLMs and optimization to create a Decision Optimization CoPilot (DOCP) - an AI tool designed to assist any decision maker, interacting in natural language to grasp the business problem, subsequently formulating and solving the corresponding optimization model. This paper outlines our DOCP vision and identifies several fundamental requirements for its implementation. We describe the state of the art through a literature survey and experiments using ChatGPT. We show that a) LLMs already provide substantial novel capabilities relevant to a DOCP, and b) major research challenges remain to be addressed. We also propose possible research directions to overcome these gaps. We also see this work as a call to action to bring together the LLM and optimization communities to pursue our vision, thereby enabling much more widespread improved decision-making.
We investigate both the theoretical and algorithmic aspects of likelihood-based methods for recovering a complex-valued signal from multiple sets of measurements, referred to as looks, affected by speckle (multiplicative) noise. Our theoretical contributions include establishing the first existing theoretical upper bound on the Mean Squared Error (MSE) of the maximum likelihood estimator under the deep image prior hypothesis. Our theoretical results capture the dependence of MSE upon the number of parameters in the deep image prior, the number of looks, the signal dimension, and the number of measurements per look. On the algorithmic side, we introduce the concept of bagged Deep Image Priors (Bagged-DIP) and integrate them with projected gradient descent. Furthermore, we show how employing Newton-Schulz algorithm for calculating matrix inverses within the iterations of PGD reduces the computational complexity of the algorithm. We will show that this method achieves the state-of-the-art performance.
Recent work on implicit neural representations (INRs) has evidenced their potential for efficiently representing and encoding conventional video content. In this paper we, for the first time, extend their application to immersive (multi-view) videos, by proposing MV-HiNeRV, a new INR-based immersive video codec. MV-HiNeRV is an enhanced version of a state-of-the-art INR-based video codec, HiNeRV, which was developed for single-view video compression. We have modified the model to learn a different group of feature grids for each view, and share the learnt network parameters among all views. This enables the model to effectively exploit the spatio-temporal and the inter-view redundancy that exists within multi-view videos. The proposed codec was used to compress multi-view texture and depth video sequences in the MPEG Immersive Video (MIV) Common Test Conditions, and tested against the MIV Test model (TMIV) that uses the VVenC video codec. The results demonstrate the superior performance of MV-HiNeRV, with significant coding gains (up to 72.33\%) over TMIV. The implementation of MV-HiNeRV is published for further development and evaluation.
This chapter delves into the critical aspects of optimizing energy efficiency (EE) in active reconfigurable intelligent surface (RIS)-assisted massive MIMO (M-MIMO) wireless communication systems. We develop a comprehensive and unified theoretical framework to analyze the boundaries of EE within M-MIMO systems integrated with active RIS while adhering to practical constraints. Our research focuses on a formulated EE optimization problem aiming to maximize the EE for active RIS-assisted M-MIMO communication systems. Our goal is to strategically find the number of active RIS elements for outperforming the EE attainable by an entirely passive RIS. Besides, the proposed novel solution has been tailored to the innovative problem. The formulation and solution design consider analytical optimization techniques, such as lagrangian dual transform (LDT) and fractional programming (FP) optimization, facilitating the effective implementation of RIS-aided M-MIMO applications in real-world settings. In particular, our results show that the proposed algorithm can provide up to 120% higher EE than the entirely passive RIS. Besides, we found that the active RIS can operate with less than half of the reflecting elements for the entirely passive RIS. Finally, in view of active RIS achieving the complete utilization of amplification power available, it should be equipped with a reasonable number of reflecting elements above N = 49.
The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.
Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that incorporates features from multiple scales. Initially, a foreground mask in a video frame is segmented into multi-scale superpixels. Then the human-like regions in the segmented area are identified by matching a set of extracted features from superpixels against learned features in a codebook. A carried object probability map is generated using the complement of the matching probabilities of superpixels to human-like regions and background information. A group of superpixels with high carried object probability and strong edge support is then merged to obtain the shape of the carried object. We applied our method to two challenging datasets, and results show that our method is competitive with or better than the state-of-the-art.
小貼士
登錄享
相關主題
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191