We describe a method for Bayesian optimization by which one may incorporate data from multiple systems whose quantitative interrelationships are unknown a priori. All general (nonreal-valued) features of the systems are associated with continuous latent variables that enter as inputs into a single metamodel that simultaneously learns the response surfaces of all of the systems. Bayesian inference is used to determine appropriate beliefs regarding the latent variables. We explain how the resulting probabilistic metamodel may be used for Bayesian optimization tasks and demonstrate its implementation on a variety of synthetic and real-world examples, comparing its performance under zero-, one-, and few-shot settings against traditional Bayesian optimization, which usually requires substantially more data from the system of interest.
Vector Institute, University of Toronto（向量研究所，多伦多大学）
Few-shot classification (FSC), the task of adapting a classifier to unseen classes given a small labeled dataset, is an important step on the path toward human-like machine learning. Bayesian methods are well-suited to tackling the fundamental issue of overfitting in the few-shot scenario because they allow practitioners to specify prior beliefs and update those beliefs in light of observed data. Contemporary approaches to Bayesian few-shot classification maintain a posterior distribution over model parameters, which is slow and requires storage that scales with model size. Instead, we propose…
Accelerating Convergence in Bayesian Few-Shot Classification
Center for Applied Statistics（应用统计中心）；School of Statistics, Renmin University of China（中国人民大学统计学院）；Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing（北京未来区块链与隐私计算高精尖创新中心）
University of Edinburgh（爱丁堡大学）；School of Informatics（信息学院）；School of Engineering（工程学院）
Recently, different machine learning methods have been introduced to tackle the challenging few-shot learning scenario that is, learning from a small labeled dataset related to a specific task. Common approaches have taken the form of meta-learning: learning to learn on the new problem given the old. Following the recognition that meta-learning is implementing learning in a multi-level model, we present a Bayesian treatment for the meta-learning inner loop through the use of deep kernels. As a result we can learn a kernel that transfers to new tasks; we call this Deep Kernel Transfer (DKT). Th…
Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；University of Montréal（蒙特利尔大学）；Tsinghua University（清华大学）；HEC Montréal（蒙特利尔高等商学院）
This paper studies few-shot relation extraction, which aims at predicting the relation for a pair of entities in a sentence by training with a few labeled examples in each relation. To more effectively generalize to new relations, in this paper we study the relationships between different relations and propose to leverage a global relation graph. We propose a novel Bayesian meta-learning approach to effectively learn the posterior distribution of the prototype vectors of relations, where the initial prior of the prototype vectors is parameterized with a graph neural network on the global relat…
Bayesian optimization (BO) is a popular approach to optimize expensive-to-evaluate black-box functions. A significant challenge in BO is to scale to high-dimensional parameter spaces while retaining sample efficiency. A solution considered in existing literature is to embed the high-dimensional space in a lower-dimensional manifold, often via a random linear embedding. In this paper, we identify several crucial issues and misconceptions about the use of linear embeddings for BO. We study the properties of linear embeddings from the literature and show that some of the design choices in current…
University of Oxford（牛津大学）；University of Freiburg（弗赖堡大学）；University of Amsterdam（阿姆斯特丹大学）；University of British Columbia（不列颠哥伦比亚大学）；Canadian Institute for Advanced Research（加拿大高等研究院）
Bayesian optimization techniques have been successfully applied to robotics, planning, sensor placement, recommendation, advertising, intelligent user interfaces and automatic algorithm configuration. Despite these successes, the approach is restricted to problems of moderate dimension, and several workshops on Bayesian optimization have identified its scaling to high-dimensions as one of the holy grails of the field. In this paper, we introduce a novel random embedding idea to attack this problem. The resulting Random EMbedding Bayesian Optimization (REMBO) algorithm is very simple, has impor…
As machine learning algorithms are increasingly deployed for high-impact automated decision making, ethical and increasingly also legal standards demand that they treat all individuals fairly, without discrimination based on their age, gender, race or other sensitive traits. In recent years much progress has been made on ensuring fairness and reducing bias in standard machine learning settings. Yet, for network embedding, with applications in vulnerable domains ranging from social network analysis to recommender systems, current options remain limited both in number and performance. We thus pr…
University of Sydney（悉尼大学）；CSIRO（澳大利亚联邦科学与工业研究组织）；NVIDIA（英伟达）
Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying function of interest whose conditional mean was observed is a challenging inference task. We formalize deconditional kernel mean embeddings as a solution to this inverse problem, and show that it can be naturally viewed as a nonparametric Bayes' rule. Critically, we introduce the notion of task transformed Gaussian processes and establish deconditional kernel …
The University of Sydney（悉尼大学）；CSIRO（澳大利亚联邦科学与工业研究组织）；NVIDIA（英伟达）
In likelihood-free settings where likelihood evaluations are intractable, approximate Bayesian computation (ABC) addresses the formidable inference task to discover plausible parameters of simulation programs that explain the observations. However, they demand large quantities of simulation calls. Critically, hyperparameters that determine measures of simulation discrepancy crucially balance inference accuracy and sample efficiency, yet are difficult to tune. In this paper, we present kernel embedding likelihood-free inference (KELFI), a holistic framework that automatically learns model hyper…
We present BOFFIN TTS (Bayesian Optimization For FIne-tuning Neural Text To Speech), a novel approach for few-shot speaker adaptation. Here, the task is to fine-tune a pre-trained TTS model to mimic a new speaker using a small corpus of target utterances. We demonstrate that there does not exist a one-size-fits-all adaptation strategy, with convincing synthesis requiring a corpus-specific configuration of the hyper-parameters that control fine-tuning. By using Bayesian optimization to efficiently optimize these hyper-parameter values for a target speaker, we are able to perform adaptation with…
Washington University（华盛顿大学）；Facebook（脸书）；University of Pennsylvania（宾夕法尼亚大学）
Bayesian optimization is a sequential decision making framework for optimizing expensive-to-evaluate black-box functions. Computing a full lookahead policy amounts to solving a highly intractable stochastic dynamic program. Myopic approaches, such as expected improvement, are often adopted in practice, but they ignore the long-term impact of the immediate decision. Existing nonmyopic approaches are mostly heuristic and/or computationally expensive. In this paper, we provide the first efficient implementation of general multi-step lookahead Bayesian optimization, formulated as a sequence of nes…
University of Exeter（埃克塞特大学）；Swansea University（斯旺西大学）
Bayesian optimisation is a popular, surrogate model-based approach for optimising expensive black-box functions. Given a surrogate model, the next location to expensively evaluate is chosen via maximisation of a cheap-to-query acquisition function. We present an $ε$-greedy procedure for Bayesian optimisation in batch settings in which the black-box function can be evaluated multiple times in parallel. Our $ε$-shotgun algorithm leverages the model's prediction, uncertainty, and the approximated rate of change of the landscape to determine the spread of batch solutions to be distributed around a…
The University of Tokyo（东京大学）；Austrian Academy of Sciences（奥地利科学院）；Technische Universität Wien（维也纳工业大学）
Optimizing parameterized quantum circuits is a key routine in using near-term quantum devices. However, the existing algorithms for such optimization require an excessive number of quantum-measurement shots for estimating expectation values of observables and repeating many iterations, whose cost has been a critical obstacle for practical use. We develop an efficient alternative optimization algorithm, stochastic gradient line Bayesian optimization (SGLBO), to address this problem. SGLBO reduces the measurement-shot cost by estimating an appropriate direction of updating circuit parameters bas…
State Key Laboratory for Novel Software Technology（新型软件技术国家重点实验室）；Nanjing University（南京大学）
Bayesian optimization is a broadly applied methodology to optimize the expensive black-box function. Despite its success, it still faces the challenge from the high-dimensional search space. To alleviate this problem, we propose a novel Bayesian optimization framework (termed SILBO), which finds a low-dimensional space to perform Bayesian optimization iteratively through semi-supervised dimension reduction. SILBO incorporates both labeled points and unlabeled points acquired from the acquisition function to guide the embedding space learning. To accelerate the learning procedure, we present a …
IBM Research（IBM研究院）；University of Freiburg（弗莱堡大学）
Hyperparameter optimization (HPO) is a central pillar in the automation of machine learning solutions and is mainly performed via Bayesian optimization, where a parametric surrogate is learned to approximate the black box response function (e.g. validation error). Unfortunately, evaluating the response function is computationally intensive. As a remedy, earlier work emphasizes the need for transfer learning surrogates which learn to optimize hyperparameters for an algorithm from other tasks. In contrast to previous work, we propose to rethink HPO as a few-shot learning problem in which we trai…
Leiden Institute of Advanced Computer Science（莱顿高级计算机科学研究所）；Leiden University（莱顿大学）
Bayesian Optimization is methodology used in statistical modelling that utilizes a Gaussian process prior distribution to iteratively update a posterior distribution towards the true distribution of the data. Finding unbiased informative priors to sample from is challenging and can greatly influence the outcome on the posterior distribution if only few data are available. In this paper we propose a novel approach to utilize meta-learning to automate the estimation of informative conjugate prior distributions given a distribution class. From this process we generate priors that require only few…
National Chiao Tung University（国立交通大学）；Facebook AI（脸书人工智能研究院）
Bayesian optimization (BO) conventionally relies on handcrafted acquisition functions (AFs) to sequentially determine the sample points. However, it has been widely observed in practice that the best-performing AF in terms of regret can vary significantly under different types of black-box functions. It has remained a challenge to design one AF that can attain the best performance over a wide variety of black-box functions. This paper aims to attack this challenge through the perspective of reinforced few-shot AF learning (FSAF). Specifically, we first connect the notion of AFs with Q-function…
State University of New York at Buffalo（纽约州立大学布法罗分校）；University of California, Irvine（加州大学欧文分校）
Current state-of-the-art nonparametric Bayesian text clustering methods model documents through multinomial distribution on bags of words. Although these methods can effectively utilize the word burstiness representation of documents and achieve decent performance, they do not explore the sequential information of text and relationships among synonyms. In this paper, the documents are modeled as the joint of bags of words, sequential features and word embeddings. We proposed Sequential Embedding induced Dirichlet Process Mixture Model (SiDPMM) to effectively exploit this joint document represe…
Indiana University Purdue University Indianapolis（印第安纳大学与普渡大学印第安纳波利斯联合分校）；Facebook Inc.（脸书公司）；IBM Research（IBM研究院）
Network embedding methodologies, which learn a distributed vector representation for each vertex in a network, have attracted considerable interest in recent years. Existing works have demonstrated that vertex representation learned through an embedding method provides superior performance in many real-world applications, such as node classification, link prediction, and community detection. However, most of the existing methods for network embedding only utilize topological information of a vertex, ignoring a rich set of nodal attributes (such as, user profiles of an online social network, or…
In a traditional setting, classifiers are trained to approximate a target function $f:X \rightarrow Y$ where at least a sample for each $y \in Y$ is presented to the training algorithm. In a zero-shot setting we have a subset of the labels $\hat{Y} \subset Y$ for which we do not observe any corresponding training instance. Still, the function $f$ that we train must be able to correctly assign labels also on $\hat{Y}$. In practice, zero-shot problems are very important especially when the label set is large and the cost of editorially label samples for all possible values in the label set might…
This works extends the Random Embedding Bayesian Optimization approach by integrating a warping of the high dimensional subspace within the covariance kernel. The proposed warping, that relies on elementary geometric considerations, allows mitigating the drawbacks of the high extrinsic dimensionality while avoiding the algorithm to evaluate points giving redundant information. It also alleviates constraints on bound selection for the embedded domain, thus improving the robustness, as illustrated with a test case with 25 variables and intrinsic dimension 6.
For assistive robots and virtual agents to achieve ubiquity, machines will need to anticipate the needs of their human counterparts. The field of Learning from Demonstration (LfD) has sought to enable machines to infer predictive models of human behavior for autonomous robot control. However, humans exhibit heterogeneity in decision-making, which traditional LfD approaches fail to capture. To overcome this challenge, we propose a Bayesian LfD framework to infer an integrated representation of all human task demonstrators by inferring human-specific embeddings, thereby distilling their unique c…
Kernel methods are one of the mainstays of machine learning, but the problem of kernel learning remains challenging, with only a few heuristics and very little theory. This is of particular importance in methods based on estimation of kernel mean embeddings of probability measures. For characteristic kernels, which include most commonly used ones, the kernel mean embedding uniquely determines its probability measure, so it can be used to design a powerful statistical testing framework, which includes nonparametric two-sample and independence tests. In practice, however, the performance of thes…
In this paper, we develop a group learning approach to analyze the underlying heterogeneity structure of shot selection among professional basketball players in the NBA. We propose a mixture of finite mixtures (MFM) model to capture the heterogeneity of shot selection among different players based on Log Gaussian Cox process (LGCP). Our proposed method can simultaneously estimate the number of groups and group configurations. An efficient Markov Chain Monte Carlo (MCMC) algorithm is developed for our proposed model. Simulation studies have been conducted to demonstrate its performance. Ultimat…
Basketball shot location data provide valuable summary information regarding players to coaches, sports analysts, fans, statisticians, as well as players themselves. Represented by spatial points, such data are naturally analyzed with spatial point process models. We present a novel nonparametric Bayesian method for learning the underlying intensity surface built upon a combination of Dirichlet process and Markov random field. Our method has the advantage of effectively encouraging local spatial homogeneity when estimating a globally heterogeneous intensity surface. Posterior inferences are pe…
Social scientists have recently turned to analyzing text using tools from natural language processing like word embeddings to measure concepts like ideology, bias, and affinity. However, word embeddings are difficult to use in the regression framework familiar to social scientists: embeddings are are neither identified, nor directly interpretable. I offer two advances on standard embedding models to remedy these problems. First, I develop Bayesian Word Embeddings with Automatic Relevance Determination priors, relaxing the assumption that all embedding dimensions have equal weight. Second, I ap…
In this paper we propose a new sampling-free approach to solve Bayesian model inversion problems that is an extension of the previously proposed spectral likelihood expansions (SLE) method. Our approach, called stochastic spectral likelihood embedding (SSLE), uses the recently presented stochastic spectral embedding (SSE) method for local spectral expansion refinement to approximate the likelihood function at the core of Bayesian inversion problems. We show that, similar to SLE, this approach results in analytical expressions for key statistics of the Bayesian posterior distribution, such as e…
We propose a Bayesian approach, called the posterior spectral embedding, for estimating the latent positions in random dot product graphs, and prove its optimality. Unlike the classical spectral-based adjacency/Laplacian spectral embedding, the posterior spectral embedding is a fully-likelihood based graph estimation method taking advantage of the Bernoulli likelihood information of the observed adjacency matrix. We develop a minimax-lower bound for estimating the latent positions, and show that the posterior spectral embedding achieves this lower bound since it both results in a minimax-optim…
We present a compositional embedding framework that infers not just a single class per input image, but a set of classes, in the setting of one-shot learning. Specifically, we propose and evaluate several novel models consisting of (1) an embedding function f trained jointly with a "composition" function g that computes set union operations between the classes encoded in two embedding vectors; and (2) embedding f trained jointly with a "query" function h that computes whether the classes encoded in one embedding subsume the classes encoded in another embedding. In contrast to prior work, these…
In this paper we present the first baseline results for the task of few-shot learning of discrete embedding vectors for image recognition. Few-shot learning is a highly researched task, commonly leveraged by recognition systems that are resource constrained to train on a small number of images per class. Few-shot systems typically store a continuous embedding vector of each class, posing a risk to privacy where system breaches or insider threats are a concern. Using discrete embedding vectors, we devise a simple cryptographic protocol, which uses one-way hash functions in order to build recogn…
Zero-shot learning transfers knowledge from seen classes to novel unseen classes to reduce human labor of labelling data for building new classifiers. Much effort on zero-shot learning however has focused on the standard multi-class setting, the more challenging multi-label zero-shot problem has received limited attention. In this paper we propose a transfer-aware embedding projection approach to tackle multi-label zero-shot learning. The approach projects the label embedding vectors into a low-dimensional space to induce better inter-label relationships and explicitly facilitate information t…
Pacific Northwest National Laboratory（太平洋西北国家实验室）；Seattle Research Center（西雅图研究中心）
Learning high quality class representations from few examples is a key problem in metric-learning approaches to few-shot learning. To accomplish this, we introduce a novel architecture where class representations are conditioned for each few-shot trial based on a target image. We also deviate from traditional metric-learning approaches by training a network to perform comparisons between classes rather than relying on a static metric comparison. This allows the network to decide what aspects of each class are important for the comparison at hand. We find that this flexible architecture works w…
Despite recent advances in its theoretical understanding, there still remains a significant gap in the ability of existing PAC-Bayesian theories on meta-learning to explain performance improvements in the few-shot learning setting, where the number of training examples in the target tasks is severely limited. This gap originates from an assumption in the existing theories which supposes that the number of training examples in the observed tasks and the number of training examples in the target tasks follow the same distribution, an assumption that rarely holds in practice. By relaxing this ass…
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 cla…
Standard deep learning systems require thousands or millions of examples to learn a concept, and cannot integrate new concepts easily. By contrast, humans have an incredible ability to do one-shot or few-shot learning. For instance, from just hearing a word used in a sentence, humans can infer a great deal about it, by leveraging what the syntax and semantics of the surrounding words tells us. Here, we draw inspiration from this to highlight a simple technique by which deep recurrent networks can similarly exploit their prior knowledge to learn a useful representation for a new word from littl…
University of Edinburgh（爱丁堡大学）；Samsung AI Centre（三星人工智能中心）；University of Chinese Academy of Sciences（中国科学院大学）
Current state-of-the-art few-shot learners focus on developing effective training procedures for feature representations, before using simple, e.g. nearest centroid, classifiers. In this paper, we take an orthogonal approach that is agnostic to the features used and focus exclusively on meta-learning the actual classifier layer. Specifically, we introduce MetaQDA, a Bayesian meta-learning generalization of the classic quadratic discriminant analysis. This setup has several benefits of interest to practitioners: meta-learning is fast and memory-efficient, without the need to fine-tune features.…
This paper proposes a zero-shot learning approach for audio classification based on the textual information about class labels without any audio samples from target classes. We propose an audio classification system built on the bilinear model, which takes audio feature embeddings and semantic class label embeddings as input, and measures the compatibility between an audio feature embedding and a class label embedding. We use VGGish to extract audio feature embeddings from audio recordings. We treat textual labels as semantic side information of audio classes, and use Word2Vec to generate clas…
We propose a method for learning embeddings for few-shot learning that is suitable for use with any number of ways and any number of shots (shot-free). Rather than fixing the class prototypes to be the Euclidean average of sample embeddings, we allow them to live in a higher-dimensional space (embedded class models) and learn the prototypes along with the model parameters. The class representation function is defined implicitly, which allows us to deal with a variable number of shots per each class with a simple constant-size architecture. The class embedding encompasses metric learning, that …
Several recent publications have proposed methods for mapping images into continuous semantic embedding spaces. In some cases the embedding space is trained jointly with the image transformation. In other cases the semantic embedding space is established by an independent natural language processing task, and then the image transformation into that space is learned in a second stage. Proponents of these image embedding systems have stressed their advantages over the traditional \nway{} classification framing of image understanding, particularly in terms of the promise for zero-shot learning --…
In this paper we improve the image embeddings generated in the graph neural network solution for few shot learning. We propose alternate architectures for existing networks such as Inception-Net, U-Net, Attention U-Net, and Squeeze-Net to generate embeddings and increase the accuracy of the models. We improve the quality of embeddings created at the cost of the time taken to generate them. The proposed implementations outperform the existing state of the art methods for 1-shot and 5-shot learning on the Omniglot dataset. The experiments involved a testing set and training set which had no comm…
Learning with limited data is a key challenge for visual recognition. Many few-shot learning methods address this challenge by learning an instance embedding function from seen classes and apply the function to instances from unseen classes with limited labels. This style of transfer learning is task-agnostic: the embedding function is not learned optimally discriminative with respect to the unseen classes, where discerning among them leads to the target task. In this paper, we propose a novel approach to adapt the instance embeddings to the target classification task with a set-to-set functio…
This paper addresses the challenge of leveraging multiple embedding spaces for multi-shop personalization, proving that zero-shot inference is possible by transferring shopping intent from one website to another without manual intervention. We detail a machine learning pipeline to train and optimize embeddings within shops first, and support the quantitative findings with additional qualitative insights. We then turn to the harder task of using learned embeddings across shops: if products from different shops live in the same vector space, user intent - as represented by regions in this space …
Few-shot learning aims at rapidly adapting to novel categories with only a handful of samples at test time, which has been predominantly tackled with the idea of meta-learning. However, meta-learning approaches essentially learn across a variety of few-shot tasks and thus still require large-scale training data with fine-grained supervision to derive a generalized model, thereby involving prohibitive annotation cost. In this paper, we advance the few-shot classification paradigm towards a more challenging scenario, i.e., cross-granularity few-shot classification, where the model observes only …
We introduce a novel method for multilingual transfer that utilizes deep contextual embeddings, pretrained in an unsupervised fashion. While contextual embeddings have been shown to yield richer representations of meaning compared to their static counterparts, aligning them poses a challenge due to their dynamic nature. To this end, we construct context-independent variants of the original monolingual spaces and utilize their mapping to derive an alignment for the context-dependent spaces. This mapping readily supports processing of a target language, improving transfer by context-aware embedd…
KTH Royal Institute of Technology（瑞典皇家理工学院）；Sony Europe B.V.（索尼欧洲公司）
Given the semantic descriptions of classes, Zero-Shot Learning (ZSL) aims to recognize unseen classes without labeled training data by exploiting semantic information, which contains knowledge between seen and unseen classes. Existing ZSL methods mainly use vectors to represent the embeddings to the semantic space. Despite the popularity, such vector representation limits the expressivity in terms of modeling the intra-class variability for each class. We address this issue by leveraging the use of distribution embeddings. More specifically, both image embeddings and class embeddings are model…
We propose a novel framework named ViOCE that integrates ontology-based background knowledge in the form of $n$-ball concept embeddings into a neural network based vision architecture. The approach consists of two components - converting symbolic knowledge of an ontology into continuous space by learning n-ball embeddings that capture properties of subsumption and disjointness, and guiding the training and inference of a vision model using the learnt embeddings. We evaluate ViOCE using the task of few-shot image classification, where it demonstrates superior performance on two standard benchma…
Recently, several works in the domain of natural language processing presented successful methods for word embedding. Among them, the Skip-Gram with negative sampling, known also as word2vec, advanced the state-of-the-art of various linguistics tasks. In this paper, we propose a scalable Bayesian neural word embedding algorithm. The algorithm relies on a Variational Bayes solution for the Skip-Gram objective and a detailed step by step description is provided. We present experimental results that demonstrate the performance of the proposed algorithm for word analogy and similarity tasks on six…
