Class imbalance poses new challenges when it comes to classifying data streams. Many algorithms recently proposed in the literature tackle this problem using a variety of data-level, algorithm-level, and ensemble approaches. However, there is a lack of standardized and agreed-upon procedures and benchmarks on how to evaluate these algorithms. This work proposes a standardized, exhaustive, and comprehensive experimental framework to evaluate algorithms in a collection of diverse and challenging imbalanced data stream scenarios. The experimental study evaluates 24 state-of-the-art data streams algorithms on 515 imbalanced data streams that combine static and dynamic class imbalance ratios, instance-level difficulties, concept drift, real-world and semi-synthetic datasets in binary and multi-class scenarios. This leads to a large-scale experimental study comparing state-of-the-art classifiers in the data stream mining domain. We discuss the advantages and disadvantages of state-of-the-art classifiers in each of these scenarios and we provide general recommendations to end-users for selecting the best algorithms for imbalanced data streams. Additionally, we formulate open challenges and future directions for this domain. Our experimental framework is fully reproducible and easy to extend with new methods. This way, we propose a standardized approach to conducting experiments in imbalanced data streams that can be used by other researchers to create complete, trustworthy, and fair evaluation of newly proposed methods. Our experimental framework can be downloaded from //github.com/canoalberto/imbalanced-streams.
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Missing data frequently occurs in datasets across various domains, such as medicine, sports, and finance. In many cases, to enable proper and reliable analyses of such data, the missing values are often imputed, and it is necessary that the method used has a low root mean square error (RMSE) between the imputed and the true values. In addition, for some critical applications, it is also often a requirement that the imputation method is scalable and the logic behind the imputation is explainable, which is especially difficult for complex methods that are, for example, based on deep learning. Based on these considerations, we propose a new algorithm named "conditional Distribution-based Imputation of Missing Values with Regularization" (DIMV). DIMV operates by determining the conditional distribution of a feature that has missing entries, using the information from the fully observed features as a basis. As will be illustrated via experiments in the paper, DIMV (i) gives a low RMSE for the imputed values compared to state-of-the-art methods; (ii) fast and scalable; (iii) is explainable as coefficients in a regression model, allowing reliable and trustable analysis, makes it a suitable choice for critical domains where understanding is important such as in medical fields, finance, etc; (iv) can provide an approximated confidence region for the missing values in a given sample; (v) suitable for both small and large scale data; (vi) in many scenarios, does not require a huge number of parameters as deep learning approaches; (vii) handle multicollinearity in imputation effectively; and (viii) is robust to the normally distributed assumption that its theoretical grounds rely on.
We study a subspace constrained version of the randomized Kaczmarz algorithm for solving large linear systems in which the iterates are confined to the space of solutions of a selected subsystem. We show that the subspace constraint leads to an accelerated convergence rate, especially when the system has structure such as having coherent rows or being approximately low-rank. On Gaussian-like random data, it results in a form of dimension reduction that effectively improves the aspect ratio of the system. Furthermore, this method serves as a building block for a second, quantile-based algorithm for the problem of solving linear systems with arbitrary sparse corruptions, which is able to efficiently exploit partial external knowledge about uncorrupted equations and achieve convergence in difficult settings such as in almost-square systems. Numerical experiments on synthetic and real-world data support our theoretical results and demonstrate the validity of the proposed methods for even more general data models than guaranteed by the theory.
This work proposes an adjacent-category autoregressive model for time series of ordinal variables. We apply this model to dendrochronological records to study the effect of climate on the intensity of spruce budworm defoliation during outbreaks in two sites in eastern Canada. The model's parameters are estimated using the maximum likelihood approach. We show that this estimator is consistent and asymptotically Gaussian distributed. We also propose a Portemanteau test for goodness-of-fit. Our study shows that the seasonal ranges of maximum daily temperatures in the spring and summer have a significant quadratic effect on defoliation. The study reveals that for both regions, a greater range of summer daily maximum temperatures is associated with lower levels of defoliation up to a threshold estimated at 22.7C (CI of 0-39.7C at 95%) in T\'emiscamingue and 21.8C (CI of 0-54.2C at 95%) for Matawinie. For Matawinie, a greater range in spring daily maximum temperatures increased defoliation, up to a threshold of 32.5C (CI of 0-80.0C). We also present a statistical test to compare the autoregressive parameter values between different fits of the model, which allows us to detect changes in the defoliation dynamics between the study sites in terms of their respective autoregression structures.
We present a constant-factor approximation algorithm for the Nash social welfare maximization problem with subadditive valuations accessible via demand queries. More generally, we propose a template for NSW optimization by solving a configuration-type LP and using a rounding procedure for (utilitarian) social welfare as a blackbox, which could be applicable to other variants of the problem.
Besov priors are nonparametric priors that can model spatially inhomogeneous functions. They are routinely used in inverse problems and imaging, where they exhibit attractive sparsity-promoting and edge-preserving features. A recent line of work has initiated the study of their asymptotic frequentist convergence properties. In the present paper, we consider the theoretical recovery performance of the posterior distributions associated to Besov-Laplace priors in the density estimation model, under the assumption that the observations are generated by a possibly spatially inhomogeneous true density belonging to a Besov space. We improve on existing results and show that carefully tuned Besov-Laplace priors attain optimal posterior contraction rates. Furthermore, we show that hierarchical procedures involving a hyper-prior on the regularity parameter lead to adaptation to any smoothness level.
Large language models based on self-attention mechanisms have achieved astonishing performances not only in natural language itself, but also in a variety of tasks of different nature. However, regarding processing language, our human brain may not operate using the same principle. Then, a debate is established on the connection between brain computation and artificial self-supervision adopted in large language models. One of most influential hypothesis in brain computation is the predictive coding framework, which proposes to minimize the prediction error by local learning. However, the role of predictive coding and the associated credit assignment in language processing remains unknown. Here, we propose a mean-field learning model within the predictive coding framework, assuming that the synaptic weight of each connection follows a spike and slab distribution, and only the distribution is trained. This meta predictive learning is successfully validated on classifying handwritten digits where pixels are input to the network in sequence, and on the toy and real language corpus. Our model reveals that most of the connections become deterministic after learning, while the output connections have a higher level of variability. The performance of the resulting network ensemble changes continuously with data load, further improving with more training data, in analogy with the emergent behavior of large language models. Therefore, our model provides a starting point to investigate the physics and biology correspondences of the language processing and the unexpected general intelligence.
The inherent nature of patient data poses several challenges. Prevalent cases amass substantial longitudinal data owing to their patient volume and consistent follow-ups, however, longitudinal laboratory data are renowned for their irregularity, temporality, absenteeism, and sparsity; In contrast, recruitment for rare or specific cases is often constrained due to their limited patient size and episodic observations. This study employed self-supervised learning (SSL) to pretrain a generalized laboratory progress (GLP) model that captures the overall progression of six common laboratory markers in prevalent cardiovascular cases, with the intention of transferring this knowledge to aid in the detection of specific cardiovascular event. GLP implemented a two-stage training approach, leveraging the information embedded within interpolated data and amplify the performance of SSL. After GLP pretraining, it is transferred for TVR detection. The proposed two-stage training improved the performance of pure SSL, and the transferability of GLP exhibited distinctiveness. After GLP processing, the classification exhibited a notable enhancement, with averaged accuracy rising from 0.63 to 0.90. All evaluated metrics demonstrated substantial superiority (p < 0.01) compared to prior GLP processing. Our study effectively engages in translational engineering by transferring patient progression of cardiovascular laboratory parameters from one patient group to another, transcending the limitations of data availability. The transferability of disease progression optimized the strategies of examinations and treatments, and improves patient prognosis while using commonly available laboratory parameters. The potential for expanding this approach to encompass other diseases holds great promise.
We introduce a general IFS Bayesian method for getting posterior probabilities from prior probabilities, and also a generalized Bayes' rule, which will contemplate a dynamical, as well as a non-dynamical setting. Given a loss function ${l}$, we detail the prior and posterior items, their consequences and exhibit several examples. Taking $\Theta$ as the set of parameters and $Y$ as the set of data (which usually provides {random samples}), a general IFS is a measurable map $\tau:\Theta\times Y \to Y$, which can be interpreted as a family of maps $\tau_\theta:Y\to Y,\,\theta\in\Theta$. The main inspiration for the results we will get here comes from a paper by Zellner (with no dynamics), where Bayes' rule is related to a principle of minimization of {information.} We will show that our IFS Bayesian method which produces posterior probabilities (which are associated to holonomic probabilities) is related to the optimal solution of a variational principle, somehow corresponding to the pressure in Thermodynamic Formalism, and also to the principle of minimization of information in Information Theory. Among other results, we present the prior dynamical elements and we derive the corresponding posterior elements via the Ruelle operator of Thermodynamic Formalism; getting in this way a form of dynamical Bayes' rule.
The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.
Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.
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