Gaussian processes (GPs) serve as flexible surrogates for complex surfaces, but buckle under the cubic cost of matrix decompositions with big training data sizes. Geospatial and machine learning communities suggest pseudo-inputs, or inducing points, as one strategy to obtain an approximation easing that computational burden. However, we show how placement of inducing points and their multitude can be thwarted by pathologies, especially in large-scale dynamic response surface modeling tasks. As remedy, we suggest porting the inducing point idea, which is usually applied globally, over to a more local context where selection is both easier and faster. In this way, our proposed methodology hybridizes global inducing point and data subset-based local GP approximation. A cascade of strategies for planning the selection of local inducing points is provided, and comparisons are drawn to related methodology with emphasis on computer surrogate modeling applications. We show that local inducing points extend their global and data-subset component parts on the accuracy--computational efficiency frontier. Illustrative examples are provided on benchmark data and a large-scale real-simulation satellite drag interpolation problem.

Large scale analysis of source code, and in particular scientific source code, holds the promise of better understanding the data science process, identifying analytical best practices, and providing insights to the builders of scientific toolkits. However, large corpora have remained unanalyzed in depth, as descriptive labels are absent and require expert domain knowledge to generate. We propose a novel weakly supervised transformer-based architecture for computing joint representations of code from both abstract syntax trees and surrounding natural language comments. We then evaluate the model on a new classification task for labeling computational notebook cells as stages in the data analysis process from data import to wrangling, exploration, modeling, and evaluation. We show that our model, leveraging only easily-available weak supervision, achieves a 38% increase in accuracy over expert-supplied heuristics and outperforms a suite of baselines. Our model enables us to examine a set of 118,000 Jupyter Notebooks to uncover common data analysis patterns. Focusing on notebooks with relationships to academic articles, we conduct the largest ever study of scientific code and find that notebook composition correlates with the citation count of corresponding papers.

Marketing mix models (MMMs) are statistical models for measuring the effectiveness of various marketing activities such as promotion, media advertisement, etc. In this research, we propose a comprehensive marketing mix model that captures the hierarchical structure and the carryover, shape and scale effects of certain marketing activities, as well as sign restrictions on certain coefficients that are consistent with common business sense. In contrast to commonly adopted approaches in practice, which estimate parameters in a multi-stage process, the proposed approach estimates all the unknown parameters/coefficients simultaneously using a constrained maximum likelihood approach and solved with the Hamiltonian Monte Carlo algorithm. We present results on real datasets to illustrate the use of the proposed solution algorithm.

The theory and practice of stochastic optimization has focused on stochastic gradient descent (SGD) in recent years, retaining the basic first-order stochastic nature of SGD while aiming to improve it via mechanisms such as averaging, momentum, and variance reduction. Improvement can be measured along various dimensions, however, and it has proved difficult to achieve improvements both in terms of nonasymptotic measures of convergence rate and asymptotic measures of distributional tightness. In this work, we consider first-order stochastic optimization from a general statistical point of view, motivating a specific form of recursive averaging of past stochastic gradients. The resulting algorithm, which we refer to as \emph{Recursive One-Over-T SGD} (ROOT-SGD), matches the state-of-the-art convergence rate among online variance-reduced stochastic approximation methods. Moreover, under slightly stronger distributional assumptions, the rescaled last-iterate of ROOT-SGD converges to a zero-mean Gaussian distribution that achieves near-optimal covariance.

In the information age, a secure and stable network environment is essential and hence intrusion detection is critical for any networks. In this paper, we propose a self-organizing map assisted deep autoencoding Gaussian mixture model (SOMDAGMM) supplemented with well-preserved input space topology for more accurate network intrusion detection. The deep autoencoding Gaussian mixture model comprises a compression network and an estimation network which is able to perform unsupervised joint training. However, the code generated by the autoencoder is inept at preserving the topology of the input space, which is rooted in the bottleneck of the adopted deep structure. A self-organizing map has been introduced to construct SOMDAGMM for addressing this issue. The superiority of the proposed SOM-DAGMM is empirically demonstrated with extensive experiments conducted upon two datasets. Experimental results show that SOM-DAGMM outperforms state-of-the-art DAGMM on all tests, and achieves up to 15.58% improvement in F1 score and with better stability.

Gradient tree boosting (GTB) (Friedman 2001; Mason, Baxter, Bartlett, and Frean 1999) has risen to prominence for regression problems after the introduction of xgboost (Chen and Guestrin 2016). The GTB model is an ensemble-type model, that consist of classification and regression trees (CART) (Breiman, Friedman, Stone, and Olshen 1984) that are learned in an iterative manner. GTB models are very flexible in that they automatically learn nonlinear relationships and interaction effects. However, with the increased flexibility of GTB models comes substantial worries of overfitting. The top performing gradient tree boosting libraries, such as xgboost, LightGBM (Ke, Meng, Finley, Wang, Chen, Ma, Ye, and Liu 2017) and catboost (Dorogush, Ershov, and Gulin 2018), all come with a large number of hyperparameters available for manual tuning to constrain the complexity of the GTB models. Training of gradient tree boosting models, in general, thus require some familiarity with both the chosen package, and the data for efficient tuning and application to the problem at hand. The main focus of the hyperparameters and tuning are to solve the following problems: - The complexity of trees: What are the topology of all the different trees?

Deciding on the unimodality of a dataset is an important problem in data analysis and statistical modeling. It allows to obtain knowledge about the structure of the dataset, ie. whether data points have been generated by a probability distribution with a single or more than one peaks. Such knowledge is very useful for several data analysis problems, such as for deciding on the number of clusters and determining unimodal projections. We propose a technique called UU-test (Unimodal Uniform test) to decide on the unimodality of a one-dimensional dataset. The method operates on the empirical cumulative density function (ecdf) of the dataset. It attempts to build a piecewise linear approximation of the ecdf that is unimodal and models the data sufficiently in the sense that the data corresponding to each linear segment follows the uniform distribution. A unique feature of this approach is that in the case of unimodality, it also provides a statistical model of the data in the form of a Uniform Mixture Model. We present experimental results in order to assess the ability of the method to decide on unimodality and perform comparisons with the well-known dip-test approach. In addition, in the case of unimodal datasets we evaluate the Uniform Mixture Models provided by the proposed method using the test set log-likelihood and the two-sample Kolmogorov-Smirnov (KS) test.

In the era of big data, a large number of text data generated by the Internet has given birth to a variety of text representation methods. In natural language processing (NLP), text representation transforms text into vectors that can be processed by computer without losing the original semantic information. However, these methods are difficult to effectively extract the semantic features among words and distinguish polysemy in language. Therefore, a text feature representation model based on convolutional neural network (CNN) and variational autoencoder (VAE) is proposed to extract the text features and apply the obtained text feature representation on the text classification tasks. CNN is used to extract the features of text vector to get the semantics among words and VAE is introduced to make the text feature space more consistent with Gaussian distribution. In addition, the output of the improved word2vec model is employed as the input of the proposed model to distinguish different meanings of the same word in different contexts. The experimental results show that the proposed model outperforms in k-nearest neighbor (KNN), random forest (RF) and support vector machine (SVM) classification algorithms.

A common task for recommender systems is to build a pro le of the interests of a user from items in their browsing history and later to recommend items to the user from the same catalog. The users' behavior consists of two parts: the sequence of items that they viewed without intervention (the organic part) and the sequences of items recommended to them and their outcome (the bandit part). In this paper, we propose Bayesian Latent Organic Bandit model (BLOB), a probabilistic approach to combine the 'or-ganic' and 'bandit' signals in order to improve the estimation of recommendation quality. The bandit signal is valuable as it gives direct feedback of recommendation performance, but the signal quality is very uneven, as it is highly concentrated on the recommendations deemed optimal by the past version of the recom-mender system. In contrast, the organic signal is typically strong and covers most items, but is not always relevant to the recommendation task. In order to leverage the organic signal to e ciently learn the bandit signal in a Bayesian model we identify three fundamental types of distances, namely action-history, action-action and history-history distances. We implement a scalable approximation of the full model using variational auto-encoders and the local re-paramerization trick. We show using extensive simulation studies that our method out-performs or matches the value of both state-of-the-art organic-based recommendation algorithms, and of bandit-based methods (both value and policy-based) both in organic and bandit-rich environments.

We tackle the problem of predicting the number of optimization steps that a pre-trained deep network needs to converge to a given value of the loss function. To do so, we leverage the fact that the training dynamics of a deep network during fine-tuning are well approximated by those of a linearized model. This allows us to approximate the training loss and accuracy at any point during training by solving a low-dimensional Stochastic Differential Equation (SDE) in function space. Using this result, we are able to predict the time it takes for Stochastic Gradient Descent (SGD) to fine-tune a model to a given loss without having to perform any training. In our experiments, we are able to predict training time of a ResNet within a 20% error margin on a variety of datasets and hyper-parameters, at a 30 to 45-fold reduction in cost compared to actual training. We also discuss how to further reduce the computational and memory cost of our method, and in particular we show that by exploiting the spectral properties of the gradients' matrix it is possible predict training time on a large dataset while processing only a subset of the samples.