Distance measures play an important role in machine learning. They provide the foundation for many popular and effective machine learning algorithms like k-nearest neighbors for supervised learning and k-means clustering for unsupervised learning. Different distance measures must be chosen and used depending on the types of the data. As such, it is important to know how to implement and calculate a range of different popular distance measures and the intuitions for the resulting scores. In this tutorial, you will discover distance measures in machine learning.

Python is one of the most popular languages used by data scientists and software developers. In this article, you'll see a line-up of the most important Python libraries for data science tasks, covering areas such as data processing, modeling, and visualization. Python is one of the most popular languages used by data scientists and software developers alike for data science tasks. It can be used to predict outcomes, automate tasks, streamline processes, and offer business intelligence insights. It's possible to work with data in vanilla Python, but there are quite a few open-source libraries that make Python data tasks much, much easier.

Unsupervised domain adaptation aims at transferring knowledge from the labeled source domain to the unlabeled target domain. Previous methods mainly learn a domain-invariant feature transformation, where the cross-domain discrepancy can be reduced. Maximum Mean Discrepancy(MMD) is the most popular statistic to measure domain discrepancy. However, these methods may suffer from two challenges. 1) MMD-based methods only measure the first-order statistic information across domains, while other useful information such as second-order statistic information has been ignored. 2) The classifier trained on the source domain may confuse to distinguish the correct class from a similar class, and the phenomenon is called class confusion. In this paper, we propose a method called \emph{Unsupervised domain adaptation with exploring more statistics and discriminative information}(MSDI), which tackle these two problems in the principle of structural risk minimization. We adopt the recently proposed statistic called MMCD to measure domain discrepancy which can capture both first-order and second-order statistics simultaneously in RKHS. Besides, we proposed to learn more discriminative features to avoid class confusion, where the inner of the classifier predictions with their transposes are used to reflect the confusion relationship between different classes. Moreover, we minimizing source empirical risk and adopt manifold regularization to explore geometry information in the target domain. MSDI learns a domain-invariant classifier in a unified learning framework incorporating the above objectives. We conduct comprehensive experiments on five real-world datasets and the results verify the effectiveness of the proposed method.

Humans can continuously learn new knowledge as their experience grows. In contrast, previous learning in deep neural networks can quickly fade out when they are trained on a new task. In this paper, we hypothesize this problem can be avoided by learning a set of generalized parameters, that are neither specific to old nor new tasks. In this pursuit, we introduce a novel meta-learning approach that seeks to maintain an equilibrium between all the encountered tasks. This is ensured by a new meta-update rule which avoids catastrophic forgetting. In comparison to previous meta-learning techniques, our approach is task-agnostic. When presented with a continuum of data, our model automatically identifies the task and quickly adapts to it with just a single update. We perform extensive experiments on five datasets in a class-incremental setting, leading to significant improvements over the state of the art methods (e.g., a 21.3% boost on CIFAR100 with 10 incremental tasks). Specifically, on large-scale datasets that generally prove difficult cases for incremental learning, our approach delivers absolute gains as high as 19.1% and 7.4% on ImageNet and MS-Celeb datasets, respectively.

The dominant approaches to text representation in natural language rely on learning embeddings on massive corpora which have convenient properties such as compositionality and distance preservation. In this paper, we develop a novel method to learn a heavy-tailed embedding with desirable regularity properties regarding the distributional tails, which allows to analyze the points far away from the distribution bulk using the framework of multivariate extreme value theory. In particular, a classifier dedicated to the tails of the proposed embedding is obtained which performance outperforms the baseline. This classifier exhibits a scale invariance property which we leverage by introducing a novel text generation method for label preserving dataset augmentation. Numerical experiments on synthetic and real text data demonstrate the relevance of the proposed framework and confirm that this method generates meaningful sentences with controllable attribute, e.g.

Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such structures) over all the outputs and latent functions for posterior approximation, which, however, can miss the strong posterior dependencies among the latent variables and hurt the inference quality. In addition, the updates of the variational parameters are inefficient and can be prohibitively expensive for a large number of outputs. To overcome these limitations, we propose a scalable variational inference algorithm for GPRN, which not only captures the abundant posterior dependencies but also is much more efficient for massive outputs. We tensorize the output space and introduce tensor/matrix-normal variational posteriors to capture the posterior correlations and to reduce the parameters. We jointly optimize all the parameters and exploit the inherent Kronecker product structure in the variational model evidence lower bound to accelerate the computation. We demonstrate the advantages of our method in several real-world applications.

Most research in Bayesian optimization (BO) has focused on direct feedback scenarios, where one has access to exact, or perturbed, values of some expensive-to-evaluate objective. This direction has been mainly driven by the use of BO in machine learning hyper-parameter configuration problems. However, in domains such as modelling human preferences, A/B tests or recommender systems, there is a need of methods that are able to replace direct feedback with preferential feedback, obtained via rankings or pairwise comparisons. In this work, we present Preferential Batch Bayesian Optimization (PBBO), a new framework that allows to find the optimum of a latent function of interest, given any type of parallel preferential feedback for a group of two or more points. We do so by using a Gaussian process model with a likelihood specially designed to enable parallel and efficient data collection mechanisms, which are key in modern machine learning. We show how the acquisitions developed under this framework generalize and augment previous approaches in Bayesian optimization, expanding the use of these techniques to a wider range of domains. An extensive simulation study shows the benefits of this approach, both with simulated functions and four real data sets.

Approximately design-unbiased model-assisted estimation is not new. It has become the standard practice in survey sampling, following many influential works such as Särndal et al. (1992), Deville and Särndal (1992). However, there lacks so far a theory, which allows one to generally incorporate the many common machine-learning (ML) techniques. For instance, according to Breit and Opsomer(2017, p. 203), they"are not aware of direct uses of random forests in a model-assisted survey estimator". Since modern ML techniques can often generate more flexible and powerful prediction models, when rich auxiliary feature data are available, the potentials are worth exploring, in any situation where the practical advantages of linear weighting are not essential compared to the efficiency gains that can be achieved by alternative nonlinear ML techniques. We propose a subsampling Rao-Blackwell(SRB) method, which enables exactly designunbiased estimation with the help of linear or nonlinear prediction models. Monte Carlo (MC) versions of the proposed method can be used in cases where exact RB method is computationally too costly.

Ridge regression is a well established regression estimator which can conveniently be adapted for classification problems. One compelling reason is probably the fact that ridge regression emits a closed-form solution thereby facilitating the training phase. However in the case of high-dimensional problems, the closed-form solution which involves inverting the regularised covariance matrix is rather expensive to compute. The high computational demand of such operation also renders difficulty in constructing ensemble of ridge regressions. In this paper, we consider learning an ensemble of ridge regressors where each regressor is trained in its own randomly projected subspace. Subspace regressors are later combined via adaptive boosting methodology. Experiments based on five high-dimensional classification problems demonstrated the effectiveness of the proposed method in terms of learning time and in some cases improved predictive performance can be observed.

We propose and analyze zeroth-order algorithms for optimization over Riemannian manifolds, where we observe only potentially noisy evaluations of the objective function. Our approach is based on estimating the Riemannian gradient from the objective function evaluations. We consider three settings for the objective function: (i) deterministic and smooth, (ii) stochastic and smooth, and (iii) composition of smooth and non-smooth parts. For each of the setting, we characterize the oracle complexity of our algorithm to obtain appropriately defined notions of $\epsilon$-stationary points. Notably, our complexities are independent of the ambient dimension of the Euclidean space in which the manifold is embedded in, and only depend on the intrinsic dimension of the manifold. As a proof of concept, we demonstrate the applicability of our method to the problem of black-box attacks to deep neural networks, by providing simulation and real-world image data based experimental results.