Deep Learning-Based Image Kernel for Inductive Transfer

We propose a method to classify images from target classes with a small number of training examples based on transfer learning from non-target classes. Without using any more information than class labels for samples from non-target classes, we train a Siamese net to estimate the probability of two images to belong to the same class. With some post-processing, output of the Siamese net can be used to form a gram matrix of a Mercer kernel. Coupled with a support vector machine (SVM), such a kernel gave reasonable classification accuracy on target classes without any fine-tuning. When the Siamese net was only partially fine-tuned using a small number of samples from the target classes, the resulting classifier outperformed the state-of-the-art and other alternatives. We share class separation capabilities and insights into the learning process of such a kernel on MNIST, Dogs vs. Cats, and CIFAR-10 datasets

Optimal Transport for Deep Joint Transfer Learning

Training a Deep Neural Network (DNN) from scratch requires a large amount of labeled data. For a classification task where only small amount of training data is available, a common solution is to perform fine-tuning on a DNN which is pre-trained with related source data. This consecutive training process is time consuming and does not consider explicitly the relatedness between different source and target tasks. In this paper, we propose a novel method to jointly fine-tune a Deep Neural Network with source data and target data. By adding an Optimal Transport loss (OT loss) between source and target classifier predictions as a constraint on the source classifier, the proposed Joint Transfer Learning Network (JTLN) can effectively learn useful knowledge for target classification from source data. Furthermore, by using different kind of metric as cost matrix for the OT loss, JTLN can incorporate different prior knowledge about the relatedness between target categories and source categories. We carried out experiments with JTLN based on Alexnet on image classification datasets and the results verify the effectiveness of the proposed JTLN in comparison with standard consecutive fine-tuning. This Joint Transfer Learning with OT loss is general and can also be applied to other kind of Neural Networks

A Simple Exponential Family Framework for Zero-Shot Learning

We present a simple generative framework for learning to predict previously unseen classes, based on estimating class-attribute-gated class-conditional distributions. We model each class-conditional distribution as an exponential family distribution and the parameters of the distribution of each seen/unseen class are defined as functions of the respective observed class attributes. These functions can be learned using only the seen class data and can be used to predict the parameters of the class-conditional distribution of each unseen class. Unlike most existing methods for zero-shot learning that represent classes as fixed embeddings in some vector space, our generative model naturally represents each class as a probability distribution. It is simple to implement and also allows leveraging additional unlabeled data from unseen classes to improve the estimates of their class-conditional distributions using transductive/semi-supervised learning. Moreover, it extends seamlessly to few-shot learning by easily updating these distributions when provided with a small number of additional labelled examples from unseen classes. Through a comprehensive set of experiments on several benchmark data sets, we demonstrate the efficacy of our framework.Comment: Accepted in ECML-PKDD 2017, 16 Pages: Code and Data are available: https://github.com/vkverma01/Zero-Shot

Transfer Metric Learning: Algorithms, Applications and Outlooks

Distance metric learning (DML) aims to find an appropriate way to reveal the underlying data relationship. It is critical in many machine learning, pattern recognition and data mining algorithms, and usually require large amount of label information (such as class labels or pair/triplet constraints) to achieve satisfactory performance. However, the label information may be insufficient in real-world applications due to the high-labeling cost, and DML may fail in this case. Transfer metric learning (TML) is able to mitigate this issue for DML in the domain of interest (target domain) by leveraging knowledge/information from other related domains (source domains). Although achieved a certain level of development, TML has limited success in various aspects such as selective transfer, theoretical understanding, handling complex data, big data and extreme cases. In this survey, we present a systematic review of the TML literature. In particular, we group TML into different categories according to different settings and metric transfer strategies, such as direct metric approximation, subspace approximation, distance approximation, and distribution approximation. A summarization and insightful discussion of the various TML approaches and their applications will be presented. Finally, we indicate some challenges and provide possible future directions.Comment: 14 pages, 5 figure

Adapted Deep Embeddings: A Synthesis of Methods for kk-Shot Inductive Transfer Learning

The focus in machine learning has branched beyond training classifiers on a single task to investigating how previously acquired knowledge in a source domain can be leveraged to facilitate learning in a related target domain, known as inductive transfer learning. Three active lines of research have independently explored transfer learning using neural networks. In weight transfer, a model trained on the source domain is used as an initialization point for a network to be trained on the target domain. In deep metric learning, the source domain is used to construct an embedding that captures class structure in both the source and target domains. In few-shot learning, the focus is on generalizing well in the target domain based on a limited number of labeled examples. We compare state-of-the-art methods from these three paradigms and also explore hybrid adapted-embedding methods that use limited target-domain data to fine tune embeddings constructed from source-domain data. We conduct a systematic comparison of methods in a variety of domains, varying the number of labeled instances available in the target domain ($k$), as well as the number of target-domain classes. We reach three principal conclusions: (1) Deep embeddings are far superior, compared to weight transfer, as a starting point for inter-domain transfer or model re-use (2) Our hybrid methods robustly outperform every few-shot learning and every deep metric learning method previously proposed, with a mean error reduction of 34% over state-of-the-art. (3) Among loss functions for discovering embeddings, the histogram loss (Ustinova & Lempitsky, 2016) is most robust. We hope our results will motivate a unification of research in weight transfer, deep metric learning, and few-shot learning

Application of Transfer Learning Approaches in Multimodal Wearable Human Activity Recognition

Through this project, we researched on transfer learning methods and their applications on real world problems. By implementing and modifying various methods in transfer learning for our problem, we obtained an insight in the advantages and disadvantages of these methods, as well as experiences in developing neural network models for knowledge transfer. Due to time constraint, we only applied a representative method for each major approach in transfer learning. As pointed out in the literature review, each method has its own assumptions, strengths and shortcomings. Thus we believe that an ensemble-learning approach combining the different methods should yield a better performance, which can be our future research focus

Learning Tensors in Reproducing Kernel Hilbert Spaces with Multilinear Spectral Penalties

We present a general framework to learn functions in tensor product reproducing kernel Hilbert spaces (TP-RKHSs). The methodology is based on a novel representer theorem suitable for existing as well as new spectral penalties for tensors. When the functions in the TP-RKHS are defined on the Cartesian product of finite discrete sets, in particular, our main problem formulation admits as a special case existing tensor completion problems. Other special cases include transfer learning with multimodal side information and multilinear multitask learning. For the latter case, our kernel-based view is instrumental to derive nonlinear extensions of existing model classes. We give a novel algorithm and show in experiments the usefulness of the proposed extensions

Fast Adaptation with Linearized Neural Networks

The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of the full network functions. Inspired by this finding, we propose a technique for embedding these inductive biases into Gaussian processes through a kernel designed from the Jacobian of the network. In this setting, domain adaptation takes the form of interpretable posterior inference, with accompanying uncertainty estimation. This inference is analytic and free of local optima issues found in standard techniques such as fine-tuning neural network weights to a new task. We develop significant computational speed-ups based on matrix multiplies, including a novel implementation for scalable Fisher vector products. Our experiments on both image classification and regression demonstrate the promise and convenience of this framework for transfer learning, compared to neural network fine-tuning. Code is available at https://github.com/amzn/xfer/tree/master/finite_ntk.Comment: AISTATS 202

Semi-supervised Deep Kernel Learning: Regression with Unlabeled Data by Minimizing Predictive Variance

Large amounts of labeled data are typically required to train deep learning models. For many real-world problems, however, acquiring additional data can be expensive or even impossible. We present semi-supervised deep kernel learning (SSDKL), a semi-supervised regression model based on minimizing predictive variance in the posterior regularization framework. SSDKL combines the hierarchical representation learning of neural networks with the probabilistic modeling capabilities of Gaussian processes. By leveraging unlabeled data, we show improvements on a diverse set of real-world regression tasks over supervised deep kernel learning and semi-supervised methods such as VAT and mean teacher adapted for regression.Comment: In Proceedings of Neural Information Processing Systems (NeurIPS) 201

On the characterization of the numbers nn such that any group of order nn has a given property PP

One of the classical problems in group theory is determining the set of positive integers $n$ such that every group of order $n$ has a particular property $P$, such as cyclic or abelian. We first present the Sylow theorems and the idea of solvable groups, both of which will be invaluable in our analysis. We then gather various solutions to this problem for cyclic, abelian, nilpotent, and supersolvable groups, as well as groups with ordered Sylow towers. This work is an exposition of known results, but it is hoped that the reader will find useful the presentation in a single account of the various tools that have been used to solve this general problem. This article claims no originality, but is meant as a synthesis of related knowledge and resources.Comment: Undergraduate Honors Thesis in Mathematic