In the big data era researchers face a series of problems. Even standard approaches/methodologies, like linear regression, can be difficult or problematic with huge volumes of data. Traditional approaches for regression in big datasets may suffer due to the large sample size, since they involve inverting huge data matrices or even because the data cannot fit to the memory. Proposed approaches are based on selecting representative subdata to run the regression. Existing approaches select the subdata using information criteria and/or properties from orthogonal arrays. In the present paper we improve existing algorithms providing a new algorithm that is based on D-optimality approach. We provide simulation evidence for its performance. Evidence about the parameters of the proposed algorithm is also provided in order to clarify the trade-offs between execution time and information gain. Real data applications are also provided.
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$l^q$-regularization has been demonstrated to be an attractive technique in machine learning and statistical modeling. It attempts to improve the generalization (prediction) capability of a machine (model) through appropriately shrinking its coefficients. The shape of a $l^q$ estimator differs in varying choices of the regularization order $q$. In particular, $l^1$ leads to the LASSO estimate, while $l^{2}$ corresponds to the smooth ridge regression. This makes the order $q$ a potential tuning parameter in applications. To facilitate the use of $l^{q}$-regularization, we intend to seek for a modeling strategy where an elaborative selection on $q$ is avoidable. In this spirit, we place our investigation within a general framework of $l^{q}$-regularized kernel learning under a sample dependent hypothesis space (SDHS). For a designated class of kernel functions, we show that all $l^{q}$ estimators for $0< q < \infty$ attain similar generalization error bounds. These estimated bounds are almost optimal in the sense that up to a logarithmic factor, the upper and lower bounds are asymptotically identical. This finding tentatively reveals that, in some modeling contexts, the choice of $q$ might not have a strong impact in terms of the generalization capability. From this perspective, $q$ can be arbitrarily specified, or specified merely by other no generalization criteria like smoothness, computational complexity, sparsity, etc..
Polynomial kernel regression is one of the standard and state-of-the-art learning strategies. However, as is well known, the choices of the degree of polynomial kernel and the regularization parameter are still open in the realm of model selection. The first aim of this paper is to develop a strategy to select these parameters. On one hand, based on the worst-case learning rate analysis, we show that the regularization term in polynomial kernel regression is not necessary. In other words, the regularization parameter can decrease arbitrarily fast when the degree of the polynomial kernel is suitable tuned. On the other hand,taking account of the implementation of the algorithm, the regularization term is required. Summarily, the effect of the regularization term in polynomial kernel regression is only to circumvent the " ill-condition" of the kernel matrix. Based on this, the second purpose of this paper is to propose a new model selection strategy, and then design an efficient learning algorithm. Both theoretical and experimental analysis show that the new strategy outperforms the previous one. Theoretically, we prove that the new learning strategy is almost optimal if the regression function is smooth. Experimentally, it is shown that the new strategy can significantly reduce the computational burden without loss of generalization capability.
Big data programming frameworks have become increasingly important for the development of applications for which performance and scalability are critical. In those complex frameworks, optimizing code by hand is hard and time-consuming, making automated optimization particularly necessary. In order to automate optimization, a prerequisite is to find suitable abstractions to represent programs; for instance, algebras based on monads or monoids to represent distributed data collections. Currently, however, such algebras do not represent recursive programs in a way which allows for analyzing or rewriting them. In this paper, we extend a monoid algebra with a fixpoint operator for representing recursion as a first class citizen and show how it enables new optimizations. Experiments with the Spark platform illustrate performance gains brought by these systematic optimizations.
Multi-party business processes rely on the collaboration of various players in a decentralized setting. Blockchain technology can facilitate the automation of these processes, even in cases where trust among participants is limited. Transactions are stored in a ledger, a replica of which is retained by every node of the blockchain network. The operations saved thereby are thus publicly accessible. While this enhances transparency, reliability, and persistence, it hinders the utilization of public blockchains for process automation as it violates typical confidentiality requirements in corporate settings. In this paper, we propose MARTSIA: A Multi-Authority Approach to Transaction Systems for Interoperating Applications. MARTSIA enables precise control over process data at the level of message parts. Based on Multi-Authority Attribute-Based Encryption (MA-ABE), MARTSIA realizes a number of desirable properties, including confidentiality, transparency, and auditability. We implemented our approach in proof-of-concept prototypes, with which we conduct a case study in the area of supply chain management. Also, we show the integration of MARTSIA with a state-of-the-art blockchain-based process execution engine to secure the data flow.
When estimating a regression model, we might have data where some labels are missing, or our data might be biased by a selection mechanism. When the response or selection mechanism is ignorable (i.e., independent of the response variable given the features) one can use off-the-shelf regression methods; in the nonignorable case one typically has to adjust for bias. We observe that privileged information (i.e. information that is only available during training) might render a nonignorable selection mechanism ignorable, and we refer to this scenario as Privilegedly Missing at Random (PMAR). We propose a novel imputation-based regression method, named repeated regression, that is suitable for PMAR. We also consider an importance weighted regression method, and a doubly robust combination of the two. The proposed methods are easy to implement with most popular out-of-the-box regression algorithms. We empirically assess the performance of the proposed methods with extensive simulated experiments and on a synthetically augmented real-world dataset. We conclude that repeated regression can appropriately correct for bias, and can have considerable advantage over weighted regression, especially when extrapolating to regions of the feature space where response is never observed.
In this paper, we develop an {\em epsilon admissible subsets} (EAS) model selection approach for performing group variable selection in the high-dimensional multivariate regression setting. This EAS strategy is designed to estimate a posterior-like, generalized fiducial distribution over a parsimonious class of models in the setting of correlated predictors and/or in the absence of a sparsity assumption. The effectiveness of our approach, to this end, is demonstrated empirically in simulation studies, and is compared to other state-of-the-art model/variable selection procedures. Furthermore, assuming a matrix-Normal linear model we show that the EAS strategy achieves {\em strong model selection consistency} in the high-dimensional setting if there does exist a sparse, true data generating set of predictors. In contrast to Bayesian approaches for model selection, our generalized fiducial approach completely avoids the problem of simultaneously having to specify arbitrary prior distributions for model parameters and penalize model complexity; our approach allows for inference directly on the model complexity. \textcolor{black}{Implementation of the method is illustrated through yeast data to identify significant cell-cycle regulating transcription factors.
This paper investigates the efficiency of the K-fold cross-validation (CV) procedure and a debiased version thereof as a means of estimating the generalization risk of a learning algorithm. We work under the general assumption of uniform algorithmic stability. We show that the K-fold risk estimate may not be consistent under such general stability assumptions, by constructing non vanishing lower bounds on the error in realistic contexts such as regularized empirical risk minimisation and stochastic gradient descent. We thus advocate the use of a debiased version of the K-fold and prove an error bound with exponential tail decay regarding this version. Our result is applicable to the large class of uniformly stable algorithms, contrarily to earlier works focusing on specific tasks such as density estimation. We illustrate the relevance of the debiased K-fold CV on a simple model selection problem and demonstrate empirically the usefulness of the promoted approach on real world classification and regression datasets.
Considering the field of functional data analysis, we developed a new Bayesian method for variable selection in function-on-scalar regression (FOSR). Our approach uses latent variables, allowing an adaptive selection since it can determine the number of variables and which ones should be selected for a function-on-scalar regression model. Simulation studies show the proposed method's main properties, such as its accuracy in estimating the coefficients and high capacity to select variables correctly. Furthermore, we conducted comparative studies with the main competing methods, such as the BGLSS method as well as the group LASSO, the group MCP and the group SCAD. We also used a COVID-19 dataset and some socioeconomic data from Brazil for real data application. In short, the proposed Bayesian variable selection model is extremely competitive, showing significant predictive and selective quality.
The usability of Reinforcement Learning is restricted by the large computation times it requires. Curriculum Reinforcement Learning speeds up learning by defining a helpful order in which an agent encounters tasks, i.e. from simple to hard. Curricula based on Absolute Learning Progress (ALP) have proven successful in different environments, but waste computation on repeating already learned behaviour in new tasks. We solve this problem by introducing a new regularization method based on Self-Paced (Deep) Learning, called Self-Paced Absolute Learning Progress (SPALP). We evaluate our method in three different environments. Our method achieves performance comparable to original ALP in all cases, and reaches it quicker than ALP in two of them. We illustrate possibilities to further improve the efficiency and performance of SPALP.
Personalized recommender systems fulfill the daily demands of customers and boost online businesses. The goal is to learn a policy that can generate a list of items that matches the user's demand or interest. While most existing methods learn a pointwise scoring model that predicts the ranking score of each individual item, recent research shows that the listwise approach can further improve the recommendation quality by modeling the intra-list correlations of items that are exposed together. This has motivated the recent list reranking and generative recommendation approaches that optimize the overall utility of the entire list. However, it is challenging to explore the combinatorial space of list actions and existing methods that use cross-entropy loss may suffer from low diversity issues. In this work, we aim to learn a policy that can generate sufficiently diverse item lists for users while maintaining high recommendation quality. The proposed solution, GFN4Rec, is a generative method that takes the insight of the flow network to ensure the alignment between list generation probability and its reward. The key advantages of our solution are the log scale reward matching loss that intrinsically improves the generation diversity and the autoregressive item selection model that captures the item mutual influences while capturing future reward of the list. As validation of our method's effectiveness and its superior diversity during active exploration, we conduct experiments on simulated online environments as well as an offline evaluation framework for two real-world datasets.
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