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Register a new userFoundations of data imbalance and solutions for a data democracy
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Added by
Ajay Kulkarni
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Dealing with imbalanced data is a prevalent problem while performing classification on the datasets. Many times, this problem contributes to bias while making decisions or implementing policies. Thus, it is vital to understand the factors which cause imbalance in the data (or class imbalance). Such hidden biases and imbalances can lead to data tyranny and a major challenge to a data democracy. In this chapter, two essential statistical elements are resolved: the degree of class imbalance and the complexity of the concept; solving such issues helps in building the foundations of a data democracy. Furthermore, statistical measures which are appropriate in these scenarios are discussed and implemented on a real-life dataset (car insurance claims). In the end, popular data-level methods such as random oversampling, random undersampling, synthetic minority oversampling technique, Tomek link, and others are implemented in Python, and their performance is compared.
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The purpose of this paper is to write a complete survey of the (spectral) manifold learning methods and nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR methods in history were respectively published in Science in 2000 in which they solve the similar reduction problem of high-dimensional data endowed with the intrinsic nonlinear structure. The intrinsic nonlinear structure is always interpreted as a concept in manifolds from geometry and topology in theoretical mathematics by computer scientists and theoretical physicists. In 2001, the concept of Manifold Learning first appears as an NLDR method called Laplacian Eigenmaps purposed by Belkin and Niyogi. In the typical manifold learning setup, the data set, also called the observation set, is distributed on or near a low dimensional manifold $M$ embedded in $mathbb{R}^D$, which yields that each observation has a $D$-dimensional representation. The goal of (spectral) manifold learning is to reduce these observations as a compact lower-dimensional representation based on the geometric information. The reduction procedure is called the (spectral) manifold learning method. In this paper, we derive each (spectral) manifold learning method with the matrix and operator representation, and we then discuss the convergence behavior of each method in a geometric uniform language. Hence, we name the survey Geometric Foundations of Data Reduction.
In analyses of rare-events, regardless of the domain of application, class-imbalance issue is intrinsic. Although the challenges are known to data experts, their explicit impact on the analytic and the decisions made based on the findings are often overlooked. This is in particular prevalent in interdisciplinary research where the theoretical aspects are sometimes overshadowed by the challenges of the application. To show-case these undesirable impacts, we conduct a series of experiments on a recently created benchmark data, named Space Weather ANalytics for Solar Flares (SWAN-SF). This is a multivariate time series dataset of magnetic parameters of active regions. As a remedy for the imbalance issue, we study the impact of data manipulation (undersampling and oversampling) and model manipulation (using class weights). Furthermore, we bring to focus the auto-correlation of time series that is inherited from the use of sliding window for monitoring flares history. Temporal coherence, as we call this phenomenon, invalidates the randomness assumption, thus impacting all sampling practices including different cross-validation techniques. We illustrate how failing to notice this concept could give an artificial boost in the forecast performance and result in misleading findings. Throughout this study we utilized Support Vector Machine as a classifier, and True Skill Statistics as a verification metric for comparison of experiments. We conclude our work by specifying the correct practice in each case, and we hope that this study could benefit researchers in other domains where time series of rare events are of interest.
The availability of large amounts of time series data, paired with the performance of deep-learning algorithms on a broad class of problems, has recently led to significant interest in the use of sequence-to-sequence models for time series forecasting. We provide the first theoretical analysis of this time series forecasting framework. We include a comparison of sequence-to-sequence modeling to classical time series models, and as such our theory can serve as a quantitative guide for practitioners choosing between different modeling methodologies.
Recent advance in diffusion models incorporates the Stochastic Differential Equation (SDE), which brings the state-of-the art performance on image generation tasks. This paper improves such diffusion models by analyzing the model at the zero diffusion time. In real datasets, the score function diverges as the diffusion time ($t$) decreases to zero, and this observation leads an argument that the score estimation fails at $t=0$ with any neural network structure. Subsequently, we introduce Unbounded Diffusion Model (UDM) that resolves the score diverging problem with an easily applicable modification to any diffusion models. Additionally, we introduce a new SDE that overcomes the theoretic and practical limitations of Variance Exploding SDE. On top of that, the introduced Soft Truncation method improves the sample quality by mitigating the loss scale issue that happens at $t=0$. We further provide a theoretic result of the proposed method to uncover the behind mechanism of the diffusion models.
Incremental gradient (IG) methods, such as stochastic gradient descent and its variants are commonly used for large scale optimization in machine learning. Despite the sustained effort to make IG methods more data-efficient, it remains an open question how to select a training data subset that can theoretically and practically perform on par with the full dataset. Here we develop CRAIG, a method to select a weighted subset (or coreset) of training data that closely estimates the full gradient by maximizing a submodular function. We prove that applying IG to this subset is guaranteed to converge to the (near)optimal solution with the same convergence rate as that of IG for convex optimization. As a result, CRAIG achieves a speedup that is inversely proportional to the size of the subset. To our knowledge, this is the first rigorous method for data-efficient training of general machine learning models. Our extensive set of experiments show that CRAIG, while achieving practically the same solution, speeds up various IG methods by up to 6x for logistic regression and 3x for training deep neural networks.
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