Large-scale Learning Problems Research Articles

Model-Free Approximate Bayesian Learning for Large-Scale Conversion Funnel Optimization

The flexibility of choosing the ad action as a function of the consumer state is critical for modern-day marketing campaigns. We study the problem of identifying the optimal sequential personalized interventions that maximize the adoption probability for a new product. We model consumer behavior by a conversion funnel that captures the state of each consumer (e.g., interaction history with the firm) and allows the consumer behavior to vary as a function of both her state and firm’s sequential interventions. We show our model captures consumer behavior with very high accuracy (out-of-sample area under the curve of over 0.95) in a real-world email marketing dataset. However, it results in a very large-scale learning problem, where the firm must learn the state-specific effects of various interventions from consumer interactions. We propose a novel attribution-based decision-making algorithm for this problem that we call model-free approximate Bayesian learning. Our algorithm inherits the interpretability and scalability of Thompson sampling for bandits and maintains an approximate belief over the value of each state-specific intervention. The belief is updated as the algorithm interacts with the consumers. Despite being an approximation to the Bayes update, we prove the asymptotic optimality of our algorithm and analyze its convergence rate. We show that our algorithm significantly outperforms traditional approaches on extensive simulations calibrated to a real-world email marketing dataset.

A mini-batch algorithm for large-scale learning problems with adaptive step size

The step size selection in stochastic optimization methods is a crucial aspect that holds significant importance in theoretical analysis and practical applications. We propose two stochastic optimization methods based on the competitive Barzilai-Borwein (BB) step size in both the inner and outer loops of the mini-batch semi-stochastic gradient descent (mS2GD) algorithm. The competitive BB step size is automatically updated using the latest and most accurate secant equation. We introduce two algorithms: mS2GD-CBB, which updates the step size in the outer loop, and mS2GD-RCBB, which updates the step size in the inner loop. We evaluate the performance of the proposed algorithms on the classical optimization problem and compare them against existing methods. Experimental results demonstrate that the methods exhibit favorable convergence properties and can effectively handle the challenges of big data arising from the fields of signal processing, statistics, and machine learning. The methods offer enhanced adaptability, flexibility, and exploration capabilities, making them promising approaches for a wide range of optimization problems.

An investigation of complex fuzzy sets for large-scale learning

Complex fuzzy sets are an extension of type-1 fuzzy sets with complex-valued membership functions. Over the last 20 years, time-series forecasting has emerged as the most important application of complex fuzzy sets, with neuro-fuzzy systems employing them shown to be accurate and compact forecasting models. In the complex fuzzy sets literature, two dominant approaches to designing forecasters can be observed: sinusoidal membership functions versus complex-valued Gaussian membership functions. To date, however, there has never been a systematic investigation that compares the performance of these two membership types (or their combination) within a common architecture.We propose a new neuro-fuzzy architecture using complex fuzzy sets that has been designed for large-scale learning problems. This architecture employs randomized learning to speed up network training. In designing this architecture, we empirically compared sinusoidal complex fuzzy sets and complex Gaussian fuzzy sets. Across multiple variations of the architecture, we find that the complex Gaussian fuzzy sets lead to significantly more accurate forecasts on moderate-to-large time series datasets, while still keeping the overall size of the network compact.

LIBS2ML: A library for scalable second order machine learning algorithms

LIBS2ML is a library based on scalable second order learning algorithms for solving large-scale problems, i.e., big data problems in machine learning. LIBS2ML has been developed using MEX files, i.e., C++ with MATLAB/Octave interface to take the advantage of both the worlds, i.e., faster learning using C++ and easy I/O using MATLAB. Most of the available libraries are either in MATLAB/Python/R which are very slow and not suitable for large-scale learning, or are in C/C++ which does not have easy ways to take input and display results. So LIBS2ML is completely unique due to its focus on the scalable second order methods, the hot research topic, and being based on MEX files. Thus it provides researchers a comprehensive environment to evaluate their ideas and it also provides machine learning practitioners an effective tool to deal with the large-scale learning problems. LIBS2ML is an open-source, highly efficient, extensible, scalable, readable, portable and easy to use library. The library can be downloaded from the URL: \url{https://github.com/jmdvinodjmd/LIBS2ML}.

Asynchronous Delayed Optimization With Time-Varying Minibatches

Large-scale learning and optimization problems are often solved in parallel. In a master-worker distributed setup, worker nodes are most often assigned fixed-sized minibatches of data points to process. However, workers may take different amounts of time to complete their per-batch calculations. To deal with such variability in processing times, an alternative approach has recently been proposed wherein each worker is assigned a fixed duration to complete the calculations associated with each batch. This fixed-time approach results in time-varying minibatch sizes and has been shown to outperform the fixed minibatch approach in synchronous optimization. In this paper we make a number of contributions in the analysis and experimental verification of such systems. First, we formally present a system model of an asynchronous optimization scheme with variable-sized minibatches and derive the expected minibatch size. Second, we show that for our fixed-time asynchronous approach, the expected gradient staleness does not depend on the number of workers contrary to existing schemes. Third, we prove that for convex smooth objective functions the asynchronous variable minibatch method achieves the optimal regret and optimality gap bounds. Finally, we run experiments comparing the performances of the asynchronous fixed-time and fixed-minibatch methods. We present results for CIFAR-10 and ImageNet.

A fast diagonal distance metric learning approach for large-scale datasets

Distance metric learning (DML) aims to learn distance metrics that reflect the interactions between features and labels. Due to the high computational complexity, existing DML models are unsuitable for large-scale datasets. This study proposes a DML approach for large-scale problems by reducing the number of variables, utilizing sparse structures of the optimization problems, and taking advantage of large-scale computation platforms. The proposed approach treats DML as a linear space transformation problem and suggests that a full DML matrix can be approximated by a diagonal matrix in many cases. We solve the diagonal DML problem along with its ℓ1 and ℓ2 regularizations via linear and quadratic programming. To facilitate large-scale learning problems, we design a MapReduce framework to build triplets, which are encapsulations of triple data points used for the optimization problem, and develop a weighting mechanism for triplets according to their contributions to the whole distance distortion. Experiments show that the proposed approach is fast in large-scale DML applications with comparable accuracy to much more time-consuming full-matrix models. Since the approach is implemented with the Scala language based on the Spark platform, it can be used directly by productive Java applications, which makes it highly practical for large-scale datasets.

Large scale multi-label learning using Gaussian processes

We introduce a Gaussian process latent factor model for multi-label classification that can capture correlations among class labels by using a small set of latent Gaussian process functions. To address computational challenges, when the number of training instances is very large, we introduce several techniques based on variational sparse Gaussian process approximations and stochastic optimization. Specifically, we apply doubly stochastic variational inference that sub-samples data instances and classes which allows us to cope with Big Data. Furthermore, we show it is possible and beneficial to optimize over inducing points, using gradient-based methods, even in very high dimensional input spaces involving up to hundreds of thousands of dimensions. We demonstrate the usefulness of our approach on several real-world large-scale multi-label learning problems.

Recognition of Large-Scale ncRNA Data Using a Novel Multitask Cross-Learning 0-Order TSK Fuzzy Classifier

Recognizing noncoding ribonucleic acid (ncRNA) data is helpful in realizing the regulation of tumor formation and certain aspects of life mechanisms, such as growth, differentiation, development, and immunity. However, the scale of ncRNA data is usually very large. Using machine learning (ML) methods to automatically analyze these data can obtain more precise results than manually analyzing these data, but the traditional ML algorithms can process only small-scale training data. To solve this problem, a novel multitask cross-learning 0-order Takagi–Sugeno–Kang fuzzy classifier (MT-CL-0-TSK-FC) is proposed that uses a multitask cross-learning mechanism to solve the large-scale learning problem of ncRNA data. In addition, the proposed MT-CL-0-TSK-FC method naturally inherits the interpretability of traditional fuzzy systems and eventually generates an interpretable rulesbased database to recognize the ncRNA data. The experimental results indicate that the proposed MT-CL-0TSK-FC method has a faster running time and better classification accuracy than traditional ML methods.

Stochastic trust region inexact Newton method for large-scale machine learning

Nowadays stochastic approximation methods are one of the major research direction to deal with the large-scale machine learning problems. From stochastic first order methods, now the focus is shifting to stochastic second order methods due to their faster convergence and availability of computing resources. In this paper, we have proposed a novel Stochastic Trust RegiOn Inexact Newton method, called as STRON, to solve large-scale learning problems which uses conjugate gradient (CG) to inexactly solve trust region subproblem. The method uses progressive subsampling in the calculation of gradient and Hessian values to take the advantage of both, stochastic and full-batch regimes. We have extended STRON using existing variance reduction techniques to deal with the noisy gradients and using preconditioned conjugate gradient (PCG) as subproblem solver, and empirically proved that they do not work as expected, for the large-scale learning problems. Finally, our empirical results prove efficacy of the proposed method against existing methods with bench marked datasets.

Deep Reinforcement Learning for User Association and Resource Allocation in Heterogeneous Cellular Networks

Heterogeneous cellular networks can offload the mobile traffic and reduce the deployment costs, which have been considered to be a promising technique in the next-generation wireless network. Due to the non-convex and combinatorial characteristics, it is challenging to obtain an optimal strategy for the joint user association and resource allocation issue. In this paper, a reinforcement learning (RL) approach is proposed to achieve the maximum long-term overall network utility while guaranteeing the quality of service requirements of user equipments (UEs) in the downlink of heterogeneous cellular networks. A distributed optimization method based on multi-agent RL is developed. Moreover, to solve the computationally expensive problem with the large action space, multi-agent deep RL method is proposed. Specifically, the state, action and reward function are defined for UEs, and dueling double deep Q-network (D3QN) strategy is introduced to obtain the nearly optimal policy. Through message passing, the distributed UEs can obtain the global state space with a small communication overhead. With the double-Q strategy and dueling architecture, D3QN can rapidly converge to a subgame perfect Nash equilibrium. Simulation results demonstrate that D3QN achieves the better performance than other RL approaches in solving large-scale learning problems.

OLLAWV: OnLine Learning Algorithm using Worst-Violators

Due to the ever-growing nature of dataset sizes, the need for scalable and accurate machine learning algorithms has become evident. Stochastic gradient descent methods are popular tools used to optimize large-scale learning problems because of their generalization performance, simplicity, and scalability. This paper proposes a novel stochastic, also known as online, learning algorithm for solving the L1 support vector machine (SVM) problem, named OnLine Learning Algorithm using Worst-Violators (OLLAWV). Unlike other stochastic methods, OLLAWV eliminates the need for specifying the maximum number of iterations and the use of a regularization term. OLLAWV uses early stopping for controlling the size of the margin instead of the regularization term. The experimental study, performed under very strict nested cross-validation (a.k.a., double resampling), evaluates and compares the performance of this proposal with state-of-the-art SVM kernel methods that have been shown to outperform traditional and widely used approaches for solving L1-SVMs such as Sequential Minimal Optimization. OLLAWV is also compared to 5 other traditional non-SVM algorithms. The results over 23 datasets show OLLAWV's superior performance in terms of accuracy, scalability, and model sparseness, making it suitable for large-scale learning.

Progressive Stochastic Learning for Noisy Labels.

Large-scale learning problems require a plethora of labels that can be efficiently collected from crowdsourcing services at low cost. However, labels annotated by crowdsourced workers are often noisy, which inevitably degrades the performance of large-scale optimizations including the prevalent stochastic gradient descent (SGD). Specifically, these noisy labels adversely affect updates of the primal variable in conventional SGD. To solve this challenge, we propose a robust SGD mechanism called progressive stochastic learning (POSTAL), which naturally integrates the learning regime of curriculum learning (CL) with the update process of vanilla SGD. Our inspiration comes from the progressive learning process of CL, namely learning from "easy" tasks to "complex" tasks. Through the robust learning process of CL, POSTAL aims to yield robust updates of the primal variable on an ordered label sequence, namely, from "reliable" labels to "noisy" labels. To realize POSTAL mechanism, we design a cluster of "screening losses," which sorts all labels from the reliable region to the noisy region. To sum up, POSTAL using screening losses ensures robust updates of the primal variable on reliable labels first, then on noisy labels incrementally until convergence. In theory, we derive the convergence rate of POSTAL realized by screening losses. Meanwhile, we provide the robustness analysis of representative screening losses. Experimental results on UCI1 simulated and Amazon Mechanical Turk crowdsourcing data sets show that the POSTAL using screening losses is more effective and robust than several existing baselines.1UCI is the abbreviation of University of California Irvine.

Predicting Product Demands for Large-scale Chain Stores with FTRL-Proximal Linear Regression

Demand prediction for large-scale chain stores is a large-scale learning problem. A solution for this kind of problems is the online learning used in areas of machine learning when it is computationally infeasible to train over the entire dataset. This paper proposes to apply an online learning algorithm, FTRL-Proximal, to an example demand prediction problem for large-scale chain stores published in an open competition. Experimental results show that the algorithm with some minor modification is better than the best single model published in the competition.

Neural class‐specific regression for face verification

Face verification is a problem approached in the literature mainly using nonlinear class-specific subspace learning techniques. While it has been shown that kernel-based Class-Specific Discriminant Analysis is able to provide excellent performance in small- and medium-scale face verification problems, its application in today's large-scale problems is difficult due to its training space and computational requirements. In this paper, generalizing our previous work on kernel-based class-specific discriminant analysis, we show that class-specific subspace learning can be cast as a regression problem. This allows us to derive linear, (reduced) kernel and neural network-based class-specific discriminant analysis methods using efficient batch and/or iterative training schemes, suited for large-scale learning problems. We test the performance of these methods in two datasets describing medium- and large-scale face verification problems.

A Novel Distributed Variant of Stochastic Gradient Descent and Its Optimization

In the age of big data, large-scale learning problems become increasingly significant. Distributed machine learning algorithms thus draw a lot of interest, particularly those based on Stochastic Gradient Descent (SGD) with variance reduction technique. In this paper, we propose and implement a distributed programming strategy for a newly developed variance-reducing SGDbased algorithm, and analyze its performance with various parameter. Moreover, a new SGD-based algorithm named BATCHVR is introduced, which computes the full-gradients required by SGD in each stage using batches in an incremental manner. Experiments on the HPC cluster, i.e. TH-1A demonstrate the effectiveness of the distributed strategy and the excellent performance of the proposed algorithm.

Optimizing Content Duration for Mobile Ads

Optimizing the number of ad clicks is a large-scale learning problem that is central to the multi-billion–dollar mobile advertising industry. There are currently several optimization methods being used, including ad mediation and ad positioning. Recently, researchers have recommended using ad refresh interval as a new method for optimizing mobile advertising. This paper applies that new method to optimize content duration for mobile ads. The result achieved from this optimization study could further increase revenue for mobile advertisers and publishers. This research has high applicability for the growing mobile advertising industry. It also lays out a solid background for future research in this promising area.

Optimizing Mobile Advertising Using Ad Refresh Interval

Optimizing the number of ad clicks is a large-scale learning problem that is central to the multi-billion dollar mobile advertising industry. There are currently several optimization methods used, including ad mediation and ad positioning. This paper proposes a new method to optimize mobile advertising by using the ad refresh interval. A new metric, which can measure and compare mobile advertising performance, takes into account time limitations. The results achieved from this optimization study could maximize revenue for mobile advertisers and publishers. This research has high applicability. It also lays out a solid background for future research in this promising area.

Nyström-based approximate kernel subspace learning

In this paper, we describe a method for the determination of a subspace of the feature space in kernel methods, which is suited to large-scale learning problems. Linear model learning in the obtained space corresponds to a nonlinear model learning process in the input space. Since the obtained feature space is determined only by exploiting properties of the training data, this approach can be used for generic nonlinear pattern recognition. That is, nonlinear data mapping can be considered to be a pre-processing step exploiting nonlinear relationships between the training data. Linear techniques can be subsequently applied in the new feature space and, thus, they can model nonlinear properties of the problem at hand. In order to appropriately address the inherent problem of kernel learning methods related to their time and memory complexities, we follow an approximate learning approach. We show that the method can lead to considerable operation speed gains and achieve very good performance. Experimental results verify our analysis.

Asynchronous Distributed Semi-Stochastic Gradient Optimization

With the recent proliferation of large-scale learning problems, there have been a lot of interest on distributed machine learning algorithms, particularly those that are based on stochastic gradient descent (SGD) and its variants. However, existing algorithms either suffer from slow convergence due to the inherent variance of stochastic gradients, or have a fast linear convergence rate but at the expense of poorer solution quality. In this paper, we combine their merits by proposing a fast distributed asynchronous SGD-based algorithm with variance reduction. A constant learning rate can be used, and it is also guaranteed to converge linearly to the optimal solution. Experiments on the Google Cloud Computing Platform demonstrate that the proposed algorithm outperforms state-of-the-art distributed asynchronous algorithms in terms of both wall clock time and solution quality.

On the kernel Extreme Learning Machine speedup

In this paper, we describe an approximate method for reducing the time and memory complexities of the kernel Extreme Learning Machine variants. We show that, by adopting a Nyström-based kernel ELM matrix approximation, we can define an ELM space exploiting properties of the kernel ELM space that can be subsequently used to apply several optimization schemes proposed in the literature for ELM network training. The resulted ELM network can achieve good performance, which is comparable to that of its standard kernel ELM counterpart, while overcoming the time and memory restrictions on kernel ELM algorithms that render their application in large-scale learning problems prohibitive.