Transfer learning, or domain adaptation, is concerned with machine learning problems in which training and testing data come from possibly different distributions (denoted as $μ$ and $μ'$, respectively). In this work, we give an information-theoretic analysis on the generalization error and the excess risk of transfer learning algorithms, following a line of work initiated by Russo and Zhou. Our results suggest, perhaps as expected, that the Kullback-Leibler (KL) divergence $D(mu||mu')$ plays an important role in characterizing the generalization error in the settings of domain adaptation. Specifically, we provide generalization error upper bounds for general transfer learning algorithms and extend the results to a specific empirical risk minimization (ERM) algorithm where data from both distributions are available in the training phase. We further apply the method to iterative, noisy gradient descent algorithms, and obtain upper bounds which can be easily calculated, only using parameters from the learning algorithms. A few illustrative examples are provided to demonstrate the usefulness of the results. In particular, our bound is tighter in specific classification problems than the bound derived using Rademacher complexity.
Transfer learning has been proven effective when within-target labeled data is scarce. A lot of works have developed successful algorithms and empirically observed positive transfer effect that improves target generalization error using source knowledge. However, theoretical analysis of transfer learning is more challenging due to the nature of the problem and thus is less studied. In this report, we do a survey of theoretical works in transfer learning and summarize key theoretical guarantees that prove the effectiveness of transfer learning. The theoretical bounds are derived using model com…
Quantifying the information content in a neural network model is essentially estimating the model's Kolmogorov complexity. Recent success of prequential coding on neural networks points to a promising path of deriving an efficient description length of a model. We propose a practical measure of the generalizable information in a neural network model based on prequential coding, which we term Information Transfer ($L_{IT}$). Theoretically, $L_{IT}$ is an estimation of the generalizable part of a model's information content. In experiments, we show that $L_{IT}$ is consistently correlated with g…
We consider a transfer-learning problem by using the parameter transfer approach, where a suitable parameter of feature mapping is learned through one task and applied to another objective task. Then, we introduce the notion of the local stability and parameter transfer learnability of parametric feature mapping,and thereby derive a learning bound for parameter transfer algorithms. As an application of parameter transfer learning, we discuss the performance of sparse coding in self-taught learning. Although self-taught learning algorithms with plentiful unlabeled data often show excellent empi…
Covariate-Elaborated Robust Partial Information Transfer with Conditional Spike-and-Slab Prior
Department of Statistics and Data Science, Fudan University（复旦大学统计与数据科学系）；Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania（宾夕法尼亚大学生物统计学、流行病学与信息学系）；Department of Statistics and Applied Probability, University of California, Santa Barbara（加州大学圣芭芭拉分校统计学与应用概率系）
Tsinghua-Berkeley Shenzhen Institute（清华-伯克利深圳学院）；Massachusetts Institute of Technology（麻省理工学院）；Stanford University（斯坦福大学）；University of California, Berkeley（加州大学伯克利分校）
Task transfer learning is a popular technique in image processing applications that uses pre-trained models to reduce the supervision cost of related tasks. An important question is to determine task transferability, i.e. given a common input domain, estimating to what extent representations learned from a source task can help in learning a target task. Typically, transferability is either measured experimentally or inferred through task relatedness, which is often defined without a clear operational meaning. In this paper, we present a novel metric, H-score, an easily-computable evaluation fu…
Transfer learning is widely used for transferring knowledge from a source domain to the target domain where the labeled data is scarce. Recently, deep transfer learning has achieved remarkable progress in various applications. However, the source and target datasets usually belong to two different organizations in many real-world scenarios, potential privacy issues in deep transfer learning are posed. In this study, to thoroughly analyze the potential privacy leakage in deep transfer learning, we first divide previous methods into three categories. Based on that, we demonstrate specific threat…
Unified Optimization of Source Weights and Transfer Quantities in Multi-Source Transfer Learning: An Asymptotic Framework
Tsinghua Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院）；School of Artificial Intelligence, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）人工智能学院）
In transfer learning, training and testing data sets are drawn from different data distributions. The transfer generalization gap is the difference between the population loss on the target data distribution and the training loss. The training data set generally includes data drawn from both source and target distributions. This work presents novel information-theoretic upper bounds on the average transfer generalization gap that capture $(i)$ the domain shift between the target data distribution $P'_Z$ and the source distribution $P_Z$ through a two-parameter family of generalized $(α_1,α_2)$…
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Emory University（埃默里大学）；University of Washington（华盛顿大学）；Georgia Institute of Technology（佐治亚理工学院）
Graph neural networks (GNNs) have achieved superior performance in various applications, but training dedicated GNNs can be costly for large-scale graphs. Some recent work started to study the pre-training of GNNs. However, none of them provide theoretical insights into the design of their frameworks, or clear requirements and guarantees towards their transferability. In this work, we establish a theoretically grounded and practically useful framework for the transfer learning of GNNs. Firstly, we propose a novel view towards the essential graph information and advocate the capturing of it as …
Supervised learning datasets often have privileged information, in the form of features which are available at training time but are not available at test time e.g. the ID of the annotator that provided the label. We argue that privileged information is useful for explaining away label noise, thereby reducing the harmful impact of noisy labels. We develop a simple and efficient method for supervised learning with neural networks: it transfers via weight sharing the knowledge learned with privileged information and approximately marginalizes over privileged information at test time. Our method,…
Software Competence Center Hagenberg（哈根贝格软件能力中心）；University of Rostock（罗斯托克大学）
In order to develop machine learning and deep learning models that take into account the guidelines and principles of trustworthy AI, a novel information theoretic trustworthy AI framework is introduced. A unified approach to "privacy-preserving interpretable and transferable learning" is considered for studying and optimizing the tradeoffs between privacy, interpretability, and transferability aspects. A variational membership-mapping Bayesian model is used for the analytical approximations of the defined information theoretic measures for privacy-leakage, interpretability, and transferabilit…
Tsinghua University（清华大学）；Huawei Technologies Co. Ltd.（华为技术有限公司）；Université de Paris（巴黎大学）
Information transfer between coupled stochastic dynamics, measured by transfer entropy and information flow, is suggested as a physical process underlying the causal relation of systems. While information transfer analysis has booming applications in both science and engineering fields, critical mysteries about its foundations remain unsolved. Fundamental yet difficult questions concern how information transfer and causal relation originate, what they depend on, how they differ from each other, and if they are created by a unified and general quantity. These questions essentially determine the…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Machine learning (ML) robustness and domain generalization are fundamentally correlated: they essentially concern data distribution shifts under adversarial and natural settings, respectively. On one hand, recent studies show that more robust (adversarially trained) models are more generalizable. On the other hand, there is a lack of theoretical understanding of their fundamental connections. In this paper, we explore the relationship between regularization and domain transferability considering different factors such as norm regularization and data augmentations (DA). We propose a general the…
Mila - Quebec AI institute（米拉-魁北克人工智能研究所）；McGill University（麦吉尔大学）；Université de Montréal（蒙特利尔大学）；BIOS Health Ltd.（BIOS健康有限公司）；CIFAR（加拿大高等研究院）；Montreal Neurological Institute（蒙特利尔神经学研究所）
When presented with a data stream of two statistically dependent variables, predicting the future of one of the variables (the target stream) can benefit from information about both its history and the history of the other variable (the source stream). For example, fluctuations in temperature at a weather station can be predicted using both temperatures and barometric readings. However, a challenge when modelling such data is that it is easy for a neural network to rely on the greatest joint correlations within the target stream, which may ignore a crucial but small information transfer from t…
Korea Advanced Institute of Science and Technology（韩国高等科学技术院）；École des Ponts ParisTech（巴黎高科桥路学院）；Amazon（亚马逊）
Transferring knowledge from a teacher neural network pretrained on the same or a similar task to a student neural network can significantly improve the performance of the student neural network. Existing knowledge transfer approaches match the activations or the corresponding hand-crafted features of the teacher and the student networks. We propose an information-theoretic framework for knowledge transfer which formulates knowledge transfer as maximizing the mutual information between the teacher and the student networks. We compare our method with existing knowledge transfer methods on both k…
Many earth science applications require data at both high spatial and temporal resolution for effective monitoring of various ecosystem resources. Due to practical limitations in sensor design, there is often a trade-off in different resolutions of spatio-temporal datasets and hence a single sensor alone cannot provide the required information. Various data fusion methods have been proposed in the literature that mainly rely on individual timesteps when both datasets are available to learn a mapping between features values at different resolutions using local relationships between pixels. Eart…
Which bits went where? Past and future transfer entropy decomposition with the information bottleneck
University of Pennsylvania（宾夕法尼亚大学）；Perelman School of Medicine, University of Pennsylvania（宾夕法尼亚大学佩雷尔曼医学院）；The Santa Fe Institute（圣塔菲研究所）；Montreal Neurological Institute, McGill University（麦吉尔大学蒙特利尔神经学研究所）
Formality style transfer is the task of converting informal sentences to grammatically-correct formal sentences, which can be used to improve performance of many downstream NLP tasks. In this work, we propose a semi-supervised formality style transfer model that utilizes a language model-based discriminator to maximize the likelihood of the output sentence being formal, which allows us to use maximization of token-level conditional probabilities for training. We further propose to maximize mutual information between source and target styles as our training objective instead of maximizing the r…
