Active Learning (AL) aims to reduce the labeling burden by interactively selecting the most informative samples from a pool of unlabeled data. While there has been extensive research on improving AL query methods in recent years, some studies have questioned the effectiveness of AL compared to emerging paradigms such as semi-supervised (Semi-SL) and self-supervised learning (Self-SL), or a simple optimization of classifier configurations. Thus, today's AL literature presents an inconsistent and contradictory landscape, leaving practitioners uncertain about whether and how to use AL in their tasks. In this work, we make the case that this inconsistency arises from a lack of systematic and realistic evaluation of AL methods. Specifically, we identify five key pitfalls in the current literature that reflect the delicate considerations required for AL evaluation. Further, we present an evaluation framework that overcomes these pitfalls and thus enables meaningful statements about the performance of AL methods. To demonstrate the relevance of our protocol, we present a large-scale empirical study and benchmark for image classification spanning various data sets, query methods, AL settings, and training paradigms. Our findings clarify the inconsistent picture in the literature and enable us to give hands-on recommendations for practitioners.

Probabilistic circuits (PCs) are a family of generative models which allows for the computation of exact likelihoods and marginals of its probability distributions. PCs are both expressive and tractable, and serve as popular choices for discrete density estimation tasks. However, large PCs are susceptible to overfitting, and only a few regularization strategies (e.g., dropout, weight-decay) have been explored. We propose HyperSPNs: a new paradigm of generating the mixture weights of large PCs using a small-scale neural network. Our framework can be viewed as a soft weight-sharing strategy, which combines the greater expressiveness of large models with the better generalization and memory-footprint properties of small models. We show the merits of our regularization strategy on two state-of-theart PC families introduced in recent literature - RAT-SPNs and EiNETs - and demonstrate generalization improvements in both models on a suite of density estimation benchmarks in both discrete and continuous domains.

For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? While this could potentially guide practitioners to improve classification and mixture proportion estimation in applications where negative unlabeled data is not available but unlabeled data is abundant, we do not believe that it will fundamentally impact how machine learning is used in a way that could conceivably be socially salient. If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? The proof primarily involves using DKW inequality [15] on pqupcqand pqppcqto show convergence to their respective means qupcqand qppcq. The main idea of the proof is to use the confidence bound derived in Lemma 1 at pcand use the fact that pcminimizes the upper confidence bound. The proof is split into two parts.

We analyze the dynamics of finite width effects in wide but finite feature learning neural networks. Starting from a dynamical mean field theory description of infinite width deep neural network kernel and prediction dynamics, we provide a characterization of the O(1/ width) fluctuations of the DMFT order parameters over random initializations of the network weights. Our results, while perturbative in width, unlike prior analyses, are non-perturbative in the strength of feature learning. In the lazy limit of network training, all kernels are random but static in time and the prediction variance has a universal form. However, in the rich, feature learning regime, the fluctuations of the kernels and predictions are dynamically coupled with a variance that can be computed self-consistently.

Based on the feedback from the reviewers, we perform the following additional experiments which 0 explore the robustness of the choice of buffer size in SGD RER, choice of step sizes for GLMtron 10 and the behavior of the said algorithms with heavy tailed noise with a similar setup as in Section 7. We first perform an experimental study about the robustness of SGD RER to the choice of buffer size in Figure 3a. Notice that the performance remains the same for a large range of buffer sizes ( 100 from to 2000). However the performance degrades when the buffer size is too large ( 10000). We believe this is the case since the number of buffers decreases as the buffer size increases and the output is averaged over too few number of iterates (In the case of B = 10000, the final output is just an average of 10 iterates). Theoretically, this largest step-size is L where Lis the largest eigenvalue of -1 the Hessian. In the case of GLMtron, it was experimentally observed that if the step size was chosen 10 to be about 1.5 times the step size reported in Section 7, the iterates diverged. Quasi Newton method essentially normalizes the gradient with the inverse of the Hessian (or rather an approximation of the Hessian) in order to let it converge faster with large step sizes. In Figure 4, we consider the same system as in Section 7 but with heavy tailed noise given by the student t distribution (scale ν = 4.1) so that the 4-th moment exists but higher moments do not. The typical behavior of Forward SGD, SGD-ER, SGD-RER and Quasi Newton methods seems to be similar to that observed in the Sub-Gaussian noise case. However, GLMtron requires much smaller step sizes to ensure convergence and hence it takes much longer.