Note that in minibatch inference methods, at each iteration, a small subset of the data is sampled from the full dataset and used to make an update; these methods take advantage of the redundancy in data to perform inexpensive updates. In this paper, coresets reduce the total dataset size by, in some sense, approximating the dataset with a smaller group of (weighted) examples. However, when coresets are used in existing inference algorithms (such as these minibatch algorithms), it seems to me that a very similar procedure will occur: a small subset of this approximate, weighted dataset will be drawn, and used to make an update. I am not convinced this would actually speed up inference (i.e. In a sense, I feel that the main thing happening here is that the data is approximated in a smaller/compressed fashion; I can see how this might help with data storage concerns, but I don't see a great justification for why it would appreciably speed inference over existing minibatch methods (especially considering a coreset must be constructed before inference can proceed, which adds additional inference time to this method). One way to demonstrate this would be with timing comparison plots that explicitly show that coresets yield faster inferences given large datasets when compared to minibatch methods---however, no direct experiments of this sort are given.

Summary: The paper proposes an alternative approach to obtaining explanations from complex ML algorithms by aiming to produce an explainable modle from the start. Recently there has been a number of works on interpretability. This work is most similar to concept-based explainability where some of the more recent ones include • Bau, David, et al. "Network Dissection: Quantifying Interpretability of Deep Visual Representations." It starts out with a linear regression model and replaces the parameters of the model with a function dependent on the input, adds an optional transformation of the input into a more low-dimensional space and a generalization of the aggregration into the output. The main novelty of this paper is the idea to start out with an intrinsically interpretable model and extending it.

The task of tuning regularization coefficients in regularized regression models with provable guarantees across problem instances still poses a significant challenge in the literature. This paper investigates the sample complexity of tuning regularization parameters in linear and logistic regressions under \ell_1 and \ell_2 -constraints in the data-driven setting. For the linear regression problem, by more carefully exploiting the structure of the dual function class, we provide a new upper bound for the pseudo-dimension of the validation loss function class, which significantly improves the best-known results on the problem. Remarkably, we also instantiate the first matching lower bound, proving our results are tight. For tuning the regularization parameters of logistic regression, we introduce a new approach to studying the learning guarantee via an approximation of the validation loss function class.

One of the major open problems in machine learning is to characterize generalization in the overparameterized regime, where most traditional generalization bounds become inconsistent even for overparameterized linear regression. In many scenarios, this failure can be attributed to obscuring the crucial interplay between the training algorithm and the underlying data distribution. This paper demonstrate that the generalization behavior of overparameterized model should be analyzed in a both data-relevant and algorithm-relevant manner. To make a formal characterization, We introduce a notion called data-algorithm compatibility, which considers the generalization behavior of the entire data-dependent training trajectory, instead of traditional last-iterate analysis. Specifically, we perform a data-dependent trajectory analysis and derive a sufficient condition for compatibility in such a setting.

We derive upper bounds for random design linear regression with dependent ( \beta -mixing) data absent any realizability assumptions. In contrast to the strictly realizable martingale noise regime, no sharp \emph{instance-optimal} non-asymptotics are available in the literature. Up to constant factors, our analysis correctly recovers the variance term predicted by the Central Limit Theorem---the noise level of the problem---and thus exhibits graceful degradation as we introduce misspecification. Past a burn-in, our result is sharp in the moderate deviations regime, and in particular does not inflate the leading order term by mixing time factors.

Recent research has observed that in machine learning optimization, gradient descent (GD) often operates at the edge of stability (EoS) [Cohen et al., 2021], where the stepsizes are set to be large, resulting in non-monotonic losses induced by the GD iterates. This paper studies the convergence and implicit bias of constant-stepsize GD for logistic regression on linearly separable data in the EoS regime. Despite the presence of local oscillations, we prove that the logistic loss can be minimized by GD with any constant stepsize over a long time scale. Furthermore, we prove that with any constant stepsize, the GD iterates tend to infinity when projected to a max-margin direction (the hard-margin SVM direction) and converge to a fixed vector that minimizes a strongly convex potential when projected to the orthogonal complement of the max-margin direction. In contrast, we also show that in the EoS regime, GD iterates may diverge catastrophically under the exponential loss, highlighting the superiority of the logistic loss.

This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order. While classical large-sample theory provides asymptotic normality of the MLE under certain conditions, such classical results are expected to fail in high-dimensions as documented for the binary logistic case in the seminal work of Sur and Candès [2019]. We address this issue in classification problems with 3 or more classes, by developing asymptotic normality and asymptotic chi-square results for the multinomial logistic MLE (also known as cross-entropy minimizer) on null covariates. Our theory leads to a new methodology to test the significance of a given feature. Extensive simulation studies on synthetic data corroborate these asymptotic results and confirm the validity of proposed p-values for testing the significance of a given feature.

We investigate theory and algorithms for pool-based active learning for multiclass classification using multinomial logistic regression. Using finite sample analysis, we prove that the Fisher Information Ratio (FIR) lower and upper bounds the excess risk. Based on our theoretical analysis, we propose an active learning algorithm that employs regret minimization to minimize the FIR. To verify our derived excess risk bounds, we conduct experiments on synthetic datasets. Furthermore, we compare FIRAL with five other methods and found that our scheme outperforms them: it consistently produces the smallest classification error in the multiclass logistic regression setting, as demonstrated through experiments on MNIST, CIFAR-10, and 50-class ImageNet.

The Naïve Mean Field (NMF) approximation is widely employed in modern Machine Learning due to the huge computational gains it bestows on the statistician. Despite its popularity in practice, theoretical guarantees for high-dimensional problems are only available under strong structural assumptions (e.g. Moreover, existing theory often does not explain empirical observations noted in the existing literature. In this paper, we take a step towards addressing these problems by deriving sharp asymptotic characterizations for the NMF approximation in high-dimensional linear regression. Our results apply to a wide class of natural priors and allow for model mismatch (i.e. the underlying statistical model can be different from the fitted model).

We consider the problem of mixed linear regression (MLR), where each observed sample belongs to one of K unknown linear models. In practical applications, the mixture of the K models may be imbalanced with a significantly different number of samples from each model. Unfortunately, most MLR methods do not perform well in such settings. Motivated by this practical challenge, in this work we propose Mix-IRLS, a novel, simple and fast algorithm for MLR with excellent performance on both balanced and imbalanced mixtures.In contrast to popular approaches that recover the K models simultaneously, Mix-IRLS does it sequentially using tools from robust regression. Empirically, beyond imbalanced mixtures, Mix-IRLS succeeds in a broad range of additional settings where other methods fail, including small sample sizes, presence of outliers, and an unknown number of models K .