Showing papers in "Journal of Machine Learning Research in 2016"

Domain-adversarial training of neural networks

Abstract: We introduce a new representation learning approach for domain adaptation, in which data at training and test time come from similar but different distributions. Our approach is directly inspired by the theory on domain adaptation suggesting that, for effective domain transfer to be achieved, predictions must be made based on features that cannot discriminate between the training (source) and test (target) domains. The approach implements this idea in the context of neural network architectures that are trained on labeled data from the source domain and unlabeled data from the target domain (no labeled target-domain data is necessary). As the training progresses, the approach promotes the emergence of features that are (i) discriminative for the main learning task on the source domain and (ii) indiscriminate with respect to the shift between the domains. We show that this adaptation behaviour can be achieved in almost any feed-forward model by augmenting it with few standard layers and a new gradient reversal layer. The resulting augmented architecture can be trained using standard backpropagation and stochastic gradient descent, and can thus be implemented with little effort using any of the deep learning packages. We demonstrate the success of our approach for two distinct classification problems (document sentiment analysis and image classification), where state-of-the-art domain adaptation performance on standard benchmarks is achieved. We also validate the approach for descriptor learning task in the context of person re-identification application.

End-to-end training of deep visuomotor policies

Abstract: Policy search methods can allow robots to learn control policies for a wide range of tasks, but practical applications of policy search often require hand-engineered components for perception, state estimation, and low-level control. In this paper, we aim to answer the following question: does training the perception and control systems jointly end-to-end provide better performance than training each component separately? To this end, we develop a method that can be used to learn policies that map raw image observations directly to torques at the robot's motors. The policies are represented by deep convolutional neural networks (CNNs) with 92,000 parameters, and are trained using a guided policy search method, which transforms policy search into supervised learning, with supervision provided by a simple trajectory-centric reinforcement learning method. We evaluate our method on a range of real-world manipulation tasks that require close coordination between vision and control, such as screwing a cap onto a bottle, and present simulated comparisons to a range of prior policy search methods.

MLlib: machine learning in apache spark

Abstract: Apache Spark is a popular open-source platform for large-scale data processing that is well-suited for iterative machine learning tasks. In this paper we present MLlib, Spark's open-source distributed machine learning library. MLLIB provides efficient functionality for a wide range of learning settings and includes several underlying statistical, optimization, and linear algebra primitives. Shipped with Spark, MLLIB supports several languages and provides a high-level API that leverages Spark's rich ecosystem to simplify the development of end-to-end machine learning pipelines. MLLIB has experienced a rapid growth due to its vibrant open-source community of over 140 contributors, and includes extensive documentation to support further growth and to let users quickly get up to speed.

On the complexity of best-arm identification in multi-armed bandit models

Abstract: The stochastic multi-armed bandit model is a simple abstraction that has proven useful in many different contexts in statistics and machine learning. Whereas the achievable limit in terms of regret minimization is now well known, our aim is to contribute to a better understanding of the performance in terms of identifying the m best arms. We introduce generic notions of complexity for the two dominant frameworks considered in the literature: fixed-budget and fixed-confidence settings. In the fixed-confidence setting, we provide the first known distribution-dependent lower bound on the complexity that involves information-theoretic quantities and holds when m ≥ 1 under general assumptions. In the specific case of two armed-bandits, we derive refined lower bounds in both the fixedcon fidence and fixed-budget settings, along with matching algorithms for Gaussian and Bernoulli bandit models. These results show in particular that the complexity of the fixed-budget setting may be smaller than the complexity of the fixed-confidence setting, contradicting the familiar behavior observed when testing fully specified alternatives. In addition, we also provide improved sequential stopping rules that have guaranteed error probabilities and shorter average running times. The proofs rely on two technical results that are of independent interest: a deviation lemma for self-normalized sums (Lemma 7) and a novel change of measure inequality for bandit models (Lemma 1).

A differential equation for modeling Nesterov's accelerated gradient method: theory and insights

Abstract: We derive a second-order ordinary differential equation (ODE) which is the limit of Nesterov's accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov's scheme and thus can serve as a tool for analysis. We show that the continuous time ODE allows for a better understanding of Nesterov's scheme. As a byproduct, we obtain a family of schemes with similar convergence rates. The ODE interpretation also suggests restarting Nesterov's scheme leading to an algorithm, which can be rigorously proven to converge at a linear rate whenever the objective is strongly convex.

CVXPY: a python-embedded modeling language for convex optimization

Abstract: CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at http://www.cvxpy.org/ under the GPL license, along with documentation and examples.

Stereo matching by training a convolutional neural network to compare image patches

Abstract: We present a method for extracting depth information from a rectified image pair. Our approach focuses on the first stage of many stereo algorithms: the matching cost computation. We approach the problem by learning a similarity measure on small image patches using a convolutional neural network. Training is carried out in a supervised manner by constructing a binary classification data set with examples of similar and dissimilar pairs of patches. We examine two network architectures for this task: one tuned for speed, the other for accuracy. The output of the convolutional neural network is used to initialize the stereo matching cost. A series of post-processing steps follow: cross-based cost aggregation, semiglobal matching, a left-right consistency check, subpixel enhancement, a median filter, and a bilateral filter. We evaluate our method on the KITTI 2012, KITTI 2015, and Middlebury stereo data sets and show that it outperforms other approaches on all three data sets.

Domain-adversarial training of neural networks

Abstract: We introduce a new representation learning approach for domain adaptation, in which data at training and test time come from similar but different distributions. Our approach is directly inspired b...

mlr: machine learning in R

Abstract: The MLR package provides a generic, object-oriented, and extensible framework for classification, regression, survival analysis and clustering for the R language It provides a unified interface to more than 160 basic learners and includes meta-algorithms and model selection techniques to improve and extend the functionality of basic learners with, eg, hyperparameter tuning, feature selection, and ensemble construction Parallel high-performance computing is natively supported The package targets practitioners who want to quickly apply machine learning algorithms, as well as researchers who want to implement, benchmark, and compare their new methods in a structured environment

Multivariate Spearman's rho for Aggregating Ranks Using Copulas

Abstract: We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Furthermore, we consider the case of extreme lists: i.e., only the rank of the best or worst elements are known. We impute missing ranks by the average value and generalise Spearman's \rho to extreme ranks. Our main contribution is the derivation of a non-parametric estimator for rank aggregation based on multivariate extensions of Spearman's \rho, which measures correlation between a set of ranked lists. Multivariate Spearman's \rho is defined using copulas, and we show that the geometric mean of normalised ranks maximises multivariate correlation. Motivated by this, we propose a weighted geometric mean approach for learning to rank which has a closed form least squares solution. When only the best or worst elements of a ranked list are known, we impute the missing ranks by the average value, allowing us to apply Spearman's \rho. Finally, we demonstrate good performance on the rank aggregation benchmarks MQ2007 and MQ2008.

Distinguishing cause from effect using observational data: methods and benchmarks

Abstract: The discovery of causal relationships from purely observational data is a fundamental problem in science. The most elementary form of such a causal discovery problem is to decide whether X causes Y or, alternatively, Y causes X, given joint observations of two variables X,Y. An example is to decide whether altitude causes temperature, or vice versa, given only joint measurements of both variables. Even under the simplifying assumptions of no confounding, no feedback loops, and no selection bias, such bivariate causal discovery problems are challenging. Nevertheless, several approaches for addressing those problems have been proposed in recent years. We review two families of such methods: methods based on Additive Noise Models (ANMs) and Information Geometric Causal Inference (IGCI). We present the benchmark CAUSEEFFECTPAIRS that consists of data for 100 different causee ffect pairs selected from 37 data sets from various domains (e.g., meteorology, biology, medicine, engineering, economy, etc.) and motivate our decisions regarding the "ground truth" causal directions of all pairs. We evaluate the performance of several bivariate causal discovery methods on these real-world benchmark data and in addition on artificially simulated data. Our empirical results on real-world data indicate that certain methods are indeed able to distinguish cause from effect using only purely observational data, although more benchmark data would be needed to obtain statistically significant conclusions. One of the best performing methods overall is the method based on Additive Noise Models that has originally been proposed by Hoyer et al. (2009), which obtains an accuracy of 63 ± 10 % and an AUC of 0.74 ± 0.05 on the real-world benchmark. As the main theoretical contribution of this work we prove the consistency of that method.

Multivariate spearman's ρ for aggregating ranks using copulas

Abstract: We study the problem of rank aggregation: given a set of ranked lists, we want to form a consensus ranking. Furthermore, we consider the case of extreme lists: i.e., only the rank of the best or worst elements are known. We impute missing ranks and generalise Spearman's ρ to extreme ranks. Our main contribution is the derivation of a non-parametric estimator for rank aggregation based on multivariate extensions of Spearman's ρ, which measures correlation between a set of ranked lists. Multivariate Spearman's ρ is defined using copulas, and we show that the geometric mean of normalised ranks maximises multivariate correlation. Motivated by this, we propose a weighted geometric mean approach for learning to rank which has a closed form least squares solution. When only the best (top-k) or worst (bottom-k) elements of a ranked list are known, we impute the missing ranks by the average value, allowing us to apply Spearman's ρ. We discuss an optimistic and pessimistic imputation of missing values, which respectively maximise and minimise correlation, and show its effect on aggregating university rankings. Finally, we demonstrate good performance on the rank aggregation benchmarks MQ2007 and MQ2008.

Benefits of depth in neural networks

Abstract: For any positive integer $k$, there exist neural networks with $\Theta(k^3)$ layers, $\Theta(1)$ nodes per layer, and $\Theta(1)$ distinct parameters which can not be approximated by networks with $\mathcal{O}(k)$ layers unless they are exponentially large --- they must possess $\Omega(2^k)$ nodes. This result is proved here for a class of nodes termed "semi-algebraic gates" which includes the common choices of ReLU, maximum, indicator, and piecewise polynomial functions, therefore establishing benefits of depth against not just standard networks with ReLU gates, but also convolutional networks with ReLU and maximization gates, sum-product networks, and boosted decision trees (in this last case with a stronger separation: $\Omega(2^{k^3})$ total tree nodes are required).

Distributed coordinate descent method for learning with big data

Abstract: In this paper we develop and analyze Hydra: HYbriD cooRdinAte descent method for solving loss minimization problems with big data. We initially partition the coordinates (features) and assign each partition to a different node of a cluster. At every iteration, each node picks a random subset of the coordinates from those it owns, independently from the other computers, and in parallel computes and applies updates to the selected coordinates based on a simple closed-form formula. We give bounds on the number of iterations sufficient to approximately solve the problem with high probability, and show how it depends on the data and on the partitioning. We perform numerical experiments with a LASSO instance described by a 3TB matrix.

Should we really use post-hoc tests based on mean-ranks?

Abstract: The statistical comparison of multiple algorithms over multiple data sets is fundamental in machine learning. This is typically carried out by the Friedman test. When the Friedman test rejects the null hypothesis, multiple comparisons are carried out to establish which are the significant differences among algorithms. The multiple comparisons are usually performed using the mean-ranks test. The aim of this technical note is to discuss the inconsistencies of the mean-ranks post-hoc test with the goal of discouraging its use in machine learning as well as in medicine, psychology, etc. We show that the outcome of the mean-ranks test depends on the pool of algorithms originally included in the experiment. In other words, the outcome of the comparison between algorithms A and B depends also on the performance of the other algorithms included in the original experiment. This can lead to paradoxical situations. For instance the difference between A and B could be declared significant if the pool comprises algorithms C, D, E and not significant if the pool comprises algorithms F, G, H. To overcome these issues, we suggest instead to perform the multiple comparison using a test whose outcome only depends on the two algorithms being compared, such as the sign-test or the Wilcoxon signed-rank test.

An emphatic approach to the problem of off-policy temporal-difference learning

Abstract: In this paper we introduce the idea of improving the performance of parametric temporal-difference (TD) learning algorithms by selectively emphasizing or de-emphasizing their updates on different time steps. In particular, we show that varying the emphasis of linear TD(γ)'s updates in a particular way causes its expected update to become stable under off-policy training. The only prior model-free TD methods to achieve this with per-step computation linear in the number of function approximation parameters are the gradient-TD family of methods including TDC, GTD(γ), and GQ(λ). Compared to these methods, our emphatic TD(λ) is simpler and easier to use; it has only one learned parameter vector and one step-size parameter. Our treatment includes general state-dependent discounting and bootstrapping functions, and a way of specifying varying degrees of interest in accurately valuing different states.

Statistical-computational tradeoffs in planted problems and submatrix localization with a growing number of clusters and submatrices

Abstract: We consider two closely related problems: planted clustering and submatrix localization. In the planted clustering problem, a random graph is generated based on an underlying cluster structure of the nodes; the task is to recover these clusters given the graph. The submatrix localization problem concerns locating hidden submatrices with elevated means inside a large real-valued random matrix. Of particular interest is the setting where the number of clusters/submatrices is allowed to grow unbounded with the problem size. These formulations cover several classical models such as planted clique, planted densest subgraph, planted partition, planted coloring, and the stochastic block model, which are widely used for studying community detection, graph clustering and bi-clustering. For both problems, we show that the space of the model parameters (cluster/submatrix size, edge probabilities and the mean of the submatrices) can be partitioned into four disjoint regions corresponding to decreasing statistical and computational complexities: (1) the impossible regime, where all algorithms fail; (2) the hard regime, where the computationally expensive Maximum Likelihood Estimator (MLE) succeeds; (3) the easy regime, where the polynomial-time convexified MLE succeeds; (4) the simple regime, where a local counting/thresholding procedure succeeds. Moreover, we show that each of these algorithms provably fails in the harder regimes. Our results establish the minimax recovery limits, which are tight up to universal constants and hold even with a growing number of clusters/submatrices, and provide order-wise stronger performance guarantees for polynomial-time algorithms than previously known. Our study demonstrates the tradeoffs between statistical and computational considerations, and suggests that the minimax limits may not be achievable by polynomial-time algorithms.

Meka: a multi-label/multi-target extension to weka

Abstract: Multi-label classification has rapidly attracted interest in the machine learning literature, and there are now a large number and considerable variety of methods for this type of learning. We present MEKA: an open-source Java framework based on the well-known WEKA library. MEKA provides interfaces to facilitate practical application, and a wealth of multi-label classifiers, evaluation metrics, and tools for multi-label experiments and development. It supports multi-label and multi-target data, including in incremental and semi-supervised contexts.

An information-theoretic analysis of Thompson sampling

Abstract: We provide an information-theoretic analysis of Thompson sampling that applies across a broad range of online optimization problems in which a decision-maker must learn from partial feedback. This analysis inherits the simplicity and elegance of information theory and leads to regret bounds that scale with the entropy of the optimal-action distribution. This strengthens preexisting results and yields new insight into how information improves performance.

Consistency and fluctuations for stochastic gradient Langevin dynamics

Abstract: Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally expensive. Both the calculation of the acceptance probability and the creation of informed proposals usually require an iteration through the whole data set. The recently proposed stochastic gradient Langevin dynamics (SGLD) method circumvents this problem by generating proposals which are only based on a subset of the data, by skipping the accept-reject step and by using decreasing step-sizes sequence (δm)m≥0. We provide in this article a rigorous mathematical framework for analysing this algorithm. We prove that, under verifiable assumptions, the algorithm is consistent, satisfies a central limit theorem (CLT) and its asymptotic bias-variance decomposition can be characterized by an explicit functional of the step-sizes sequence (δm)m≥0. We leverage this analysis to give practical recommendations for the notoriously difficult tuning of this algorithm: it is asymptotically optimal to use a step-size sequence of the type δm = m-1/3, leading to an algorithm whose mean squared error (MSE) decreases at rate O(m-1/3).

Revisiting the Nyström method for improved large-scale machine learning

Abstract: We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications Our main results consist of an empirical evaluation of the performance quality and running time of sampling and projection methods on a diverse suite of SPSD matrices Our results highlight complementary aspects of sampling versus projection methods; they characterize the effects of common data preprocessing steps on the performance of these algorithms; and they point to important differences between uniform sampling and nonuniform sampling methods based on leverage scores In addition, our empirical results illustrate that existing theory is so weak that it does not provide even a qualitative guide to practice Thus, we complement our empirical results with a suite of worst-case theoretical bounds for both random sampling and random projection methods These bounds are qualitatively superior to existing bounds--eg, improved additive-error bounds for spectral and Frobenius norm error and relative-error bounds for trace norm error--and they point to future directions to make these algorithms useful in even larger-scale machine learning applications

The benefit of multitask representation learning

Abstract: We discuss a general method to learn data representations from multiple tasks. We provide a justification for this method in both settings of multitask learning and learning-to-learn. The method is illustrated in detail in the special case of linear feature learning. Conditions on the theoretical advantage offered by multitask representation learning over independent task learning are established. In particular, focusing on the important example of half-space learning, we derive the regime in which multitask representation learning is beneficial over independent task learning, as a function of the sample size, the number of tasks and the intrinsic data dimensionality. Other potential applications of our results include multitask feature learning in reproducing kernel Hilbert spaces and multilayer, deep networks.

Combinatorial multi-armed bandit and its extension to probabilistically triggered arms

Abstract: We define a general framework for a large class of combinatorial multi-armed bandit (CMAB) problems, where subsets of base arms with unknown distributions form super arms. In each round, a super arm is played and the base arms contained in the super arm are played and their outcomes are observed. We further consider the extension in which more base arms could be probabilistically triggered based on the outcomes of already triggered arms. The reward of the super arm depends on the outcomes of all played arms, and it only needs to satisfy two mild assumptions, which allow a large class of nonlinear reward instances. We assume the availability of an offline (α β)-approximation oracle that takes the means of the outcome distributions of arms and outputs a super arm that with probability β generates an α fraction of the optimal expected reward. The objective of an online learning algorithm for CMAB is to minimize (α β)-approximation regret, which is the difference in total expected reward between the αβ fraction of expected reward when always playing the optimal super arm, and the expected reward of playing super arms according to the algorithm. We provide CUCB algorithm that achieves O(log n) distribution-dependent regret, where n is the number of rounds played, and we further provide distribution-independent bounds for a large class of reward functions. Our regret analysis is tight in that it matches the bound of UCB1 algorithm (up to a constant factor) for the classical MAB problem, and it significantly improves the regret bound in an earlier paper on combinatorial bandits with linear rewards. We apply our CMAB framework to two new applications, probabilistic maximum coverage (PMC) for online advertising and social in uence maximization for viral marketing, both having nonlinear reward structures. In particular, application to social in uence maximization requires our extension on probabilistically triggered arms.

DSA: decentralized double stochastic averaging gradient algorithm

Abstract: This paper considers optimization problems where nodes of a network have access to summands of a global objective. Each of these local objectives is further assumed to be an average of a finite set of functions. The motivation for this setup is to solve large scale machine learning problems where elements of the training set are distributed to multiple computational elements. The decentralized double stochastic averaging gradient (DSA) algorithm is proposed as a solution alternative that relies on: (i) The use of local stochastic averaging gradients. (ii) Determination of descent steps as differences of consecutive stochastic averaging gradients. Strong convexity of local functions and Lipschitz continuity of local gradients is shown to guarantee linear convergence of the sequence generated by DSA in expectation. Local iterates are further shown to approach the optimal argument for almost all realizations. The expected linear convergence of DSA is in contrast to the sublinear rate characteristic of existing methods for decentralized stochastic optimization. Numerical experiments on a logistic regression problem illustrate reductions in convergence time and number of feature vectors processed until convergence relative to these other alternatives.

Variational inference for latent variables and uncertain inputs in Gaussian processes

Abstract: The Gaussian process latent variable model (GP-LVM) provides a flexible approach for non-linear dimensionality reduction that has been widely applied. However, the current approach for training GP-LVMs is based on maximum likelihood, where the latent projection variables are maximised over rather than integrated out. In this paper we present a Bayesian method for training GP-LVMs by introducing a non-standard variational inference framework that allows to approximately integrate out the latent variables and subsequently train a GP-LVM by maximising an analytic lower bound on the exact marginal likelihood. We apply this method for learning a GP-LVM from i.i.d. observations and for learning non-linear dynamical systems where the observations are temporally correlated. We show that a benefit of the variational Bayesian procedure is its robustness to overfitting and its ability to automatically select the dimensionality of the non-linear latent space. The resulting framework is generic, flexible and easy to extend for other purposes, such as Gaussian process regression with uncertain or partially missing inputs. We demonstrate our method on synthetic data and standard machine learning benchmarks, as well as challenging real world datasets, including high resolution video data.

Bayesian optimization for likelihood-free inference of simulator-based statistical models

Abstract: Our paper deals with inferring simulator-based statistical models given some observed data. A simulator-based model is a parametrized mechanism which specifies how data are generated. It is thus also referred to as generative model. We assume that only a finite number of parameters are of interest and allow the generative process to be very general; it may be a noisy nonlinear dynamical system with an unrestricted number of hidden variables. This weak assumption is useful for devising realistic models but it renders statistical inference very difficult. The main challenge is the intractability of the likelihood function. Several likelihood-free inference methods have been proposed which share the basic idea of identifying the parameters by finding values for which the discrepancy between simulated and observed data is small. A major obstacle to using these methods is their computational cost. The cost is largely due to the need to repeatedly simulate data sets and the lack of knowledge about how the parameters affect the discrepancy. We propose a strategy which combines probabilistic modeling of the discrepancy with optimization to facilitate likelihood-free inference. The strategy is implemented using Bayesian optimization and is shown to accelerate the inference through a reduction in the number of required simulations by several orders of magnitude.

Neural autoregressive distribution estimation

Abstract: We present Neural Autoregressive Distribution Estimation (NADE) models, which are neural network architectures applied to the problem of unsupervised distribution and density estimation. They leverage the probability product rule and a weight sharing scheme inspired from restricted Boltzmann machines, to yield an estimator that is both tractable and has good generalization performance. We discuss how they achieve competitive performance in modeling both binary and real-valued observations. We also present how deep NADE models can be trained to be agnostic to the ordering of input dimensions used by the autoregressive product rule decomposition. Finally, we also show how to exploit the topological structure of pixels in images using a deep convolutional architecture for NADE.

Large scale online kernel learning

Abstract: In this paper, we present a new framework for large scale online kernel learning, making kernel methods efficient and scalable for large-scale online learning applications Unlike the regular budget online kernel learning scheme that usually uses some budget maintenance strategies to bound the number of support vectors, our framework explores a completely different approach of kernel functional approximation techniques to make the subsequent online learning task efficient and scalable Specifically, we present two different online kernel machine learning algorithms: (i) Fourier Online Gradient Descent (FOGD) algorithm that applies the random Fourier features for approximating kernel functions; and (ii) Nystrom Online Gradient Descent (NOGD) algorithm that applies the Nystrom method to approximate large kernel matrices We explore these two approaches to tackle three online learning tasks: binary classification, multi-class classification, and regression The encouraging results of our experiments on large-scale datasets validate the effectiveness and efficiency of the proposed algorithms, making them potentially more practical than the family of existing budget online kernel learning approaches

Bayesian group factor analysis with structured sparsity

Abstract: Latent factor models are the canonical statistical tool for exploratory analyses of low-dimensional linear structure for a matrix of p features across n samples. We develop a structured Bayesian group factor analysis model that extends the factor model to multiple coupled observation matrices; in the case of two observations, this reduces to a Bayesian model of canonical correlation analysis. Here, we carefully define a structured Bayesian prior that encourages both element-wise and column-wise shrinkage and leads to desirable behavior on high-dimensional data. In particular, our model puts a structured prior on the joint factor loading matrix, regularizing at three levels, which enables element-wise sparsity and unsupervised recovery of latent factors corresponding to structured variance across arbitrary subsets of the observations. In addition, our structured prior allows for both dense and sparse latent factors so that covariation among either all features or only a subset of features can be recovered. We use fast parameter-expanded expectation-maximization for parameter estimation in this model. We validate our method on simulated data with substantial structure. We show results of our method applied to three high-dimensional data sets, comparing results against a number of state-of-the-art approaches. These results illustrate useful properties of our model, including i) recovering sparse signal in the presence of dense effects; ii) the ability to scale naturally to large numbers of observations; iii) flexible observation- and factor-specific regularization to recover factors with a wide variety of sparsity levels and percentage of variance explained; and iv) tractable inference that scales to modern genomic and text data sizes.