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 Statistical Learning


Active Learning with Expected Error Reduction

arXiv.org Artificial Intelligence

Active learning has been studied extensively as a method for efficient data collection. Among the many approaches in literature, Expected Error Reduction (EER) (Roy and McCallum) has been shown to be an effective method for active learning: select the candidate sample that, in expectation, maximally decreases the error on an unlabeled set. However, EER requires the model to be retrained for every candidate sample and thus has not been widely used for modern deep neural networks due to this large computational cost. In this paper we reformulate EER under the lens of Bayesian active learning and derive a computationally efficient version that can use any Bayesian parameter sampling method (such as arXiv:1506.02142). We then compare the empirical performance of our method using Monte Carlo dropout for parameter sampling against state of the art methods in the deep active learning literature. Experiments are performed on four standard benchmark datasets and three WILDS datasets (arXiv:2012.07421). The results indicate that our method outperforms all other methods except one in the data shift scenario: a model dependent, non-information theoretic method that requires an order of magnitude higher computational cost (arXiv:1906.03671).


Engineering Monosemanticity in Toy Models

arXiv.org Artificial Intelligence

In some neural networks, individual neurons correspond to natural ``features'' in the input. Such \emph{monosemantic} neurons are of great help in interpretability studies, as they can be cleanly understood. In this work we report preliminary attempts to engineer monosemanticity in toy models. We find that models can be made more monosemantic without increasing the loss by just changing which local minimum the training process finds. More monosemantic loss minima have moderate negative biases, and we are able to use this fact to engineer highly monosemantic models. We are able to mechanistically interpret these models, including the residual polysemantic neurons, and uncover a simple yet surprising algorithm. Finally, we find that providing models with more neurons per layer makes the models more monosemantic, albeit at increased computational cost. These findings point to a number of new questions and avenues for engineering monosemanticity, which we intend to study these in future work.


Sobolev Spaces, Kernels and Discrepancies over Hyperspheres

arXiv.org Artificial Intelligence

This work provides theoretical foundations for kernel methods in the hyperspherical context. Specifically, we characterise the native spaces (reproducing kernel Hilbert spaces) and the Sobolev spaces associated with kernels defined over hyperspheres. Our results have direct consequences for kernel cubature, determining the rate of convergence of the worst case error, and expanding the applicability of cubature algorithms based on Stein's method. We first introduce a suitable characterisation on Sobolev spaces on the $d$-dimensional hypersphere embedded in $(d+1)$-dimensional Euclidean spaces. Our characterisation is based on the Fourier--Schoenberg sequences associated with a given kernel. Such sequences are hard (if not impossible) to compute analytically on $d$-dimensional spheres, but often feasible over Hilbert spheres. We circumvent this problem by finding a projection operator that allows to Fourier mapping from Hilbert into finite dimensional hyperspheres. We illustrate our findings through some parametric families of kernels.


Machine Learning for Stuttering Identification: Review, Challenges and Future Directions

arXiv.org Artificial Intelligence

Stuttering is a speech disorder during which the flow of speech is interrupted by involuntary pauses and repetition of sounds. Stuttering identification is an interesting interdisciplinary domain research problem which involves pathology, psychology, acoustics, and signal processing that makes it hard and complicated to detect. Recent developments in machine and deep learning have dramatically revolutionized speech domain, however minimal attention has been given to stuttering identification. This work fills the gap by trying to bring researchers together from interdisciplinary fields. In this paper, we review comprehensively acoustic features, statistical and deep learning based stuttering/disfluency classification methods. We also present several challenges and possible future directions.


Graph Filters for Signal Processing and Machine Learning on Graphs

arXiv.org Artificial Intelligence

Filters are fundamental in extracting information from data. For time series and image data that reside on Euclidean domains, filters are the crux of many signal processing and machine learning techniques, including convolutional neural networks. Increasingly, modern data also reside on networks and other irregular domains whose structure is better captured by a graph. To process and learn from such data, graph filters account for the structure of the underlying data domain. In this article, we provide a comprehensive overview of graph filters, including the different filtering categories, design strategies for each type, and trade-offs between different types of graph filters. We discuss how to extend graph filters into filter banks and graph neural networks to enhance the representational power; that is, to model a broader variety of signal classes, data patterns, and relationships. We also showcase the fundamental role of graph filters in signal processing and machine learning applications. Our aim is that this article serves the dual purpose of providing a unifying framework for both beginner and experienced researchers, as well as a common understanding that promotes collaborations between signal processing, machine learning, and application domains.


Improved Coresets for Euclidean $k$-Means

arXiv.org Artificial Intelligence

Given a set of $n$ points in $d$ dimensions, the Euclidean $k$-means problem (resp. the Euclidean $k$-median problem) consists of finding $k$ centers such that the sum of squared distances (resp. sum of distances) from every point to its closest center is minimized. The arguably most popular way of dealing with this problem in the big data setting is to first compress the data by computing a weighted subset known as a coreset and then run any algorithm on this subset. The guarantee of the coreset is that for any candidate solution, the ratio between coreset cost and the cost of the original instance is less than a $(1\pm \varepsilon)$ factor. The current state of the art coreset size is $\tilde O(\min(k^{2} \cdot \varepsilon^{-2},k\cdot \varepsilon^{-4}))$ for Euclidean $k$-means and $\tilde O(\min(k^{2} \cdot \varepsilon^{-2},k\cdot \varepsilon^{-3}))$ for Euclidean $k$-median. The best known lower bound for both problems is $\Omega(k \varepsilon^{-2})$. In this paper, we improve the upper bounds $\tilde O(\min(k^{3/2} \cdot \varepsilon^{-2},k\cdot \varepsilon^{-4}))$ for $k$-means and $\tilde O(\min(k^{4/3} \cdot \varepsilon^{-2},k\cdot \varepsilon^{-3}))$ for $k$-median. In particular, ours is the first provable bound that breaks through the $k^2$ barrier while retaining an optimal dependency on $\varepsilon$.


DPPIN: A Biological Repository of Dynamic Protein-Protein Interaction Network Data

arXiv.org Artificial Intelligence

In the big data era, the relationship between entries becomes more and more complex. Many graph (or network) algorithms have already paid attention to dynamic networks, which are more suitable than static ones for fitting the complex real-world scenarios with evolving structures and features. To contribute to the dynamic network representation learning and mining research, we provide a new bunch of label-adequate, dynamics-meaningful, and attribute-sufficient dynamic networks from the health domain. To be specific, in our proposed repository DPPIN, we totally have 12 individual dynamic network datasets at different scales, and each dataset is a dynamic protein-protein interaction network describing protein-level interactions of yeast cells. We hope these domain-specific node features, structure evolution patterns, and node and graph labels could inspire the regularization techniques to increase the performance of graph machine learning algorithms in a more complex setting. Also, we link potential applications with our DPPIN by designing various dynamic graph experiments, where DPPIN could indicate future research opportunities for some tasks by presenting challenges on state-of-the-art baseline algorithms. Finally, we identify future directions to improve the utility of this repository and welcome constructive inputs from the community. All resources (e.g., data and code) of this work are deployed and publicly available at https://github.com/DongqiFu/DPPIN.


New Frontiers in Graph Autoencoders: Joint Community Detection and Link Prediction

arXiv.org Artificial Intelligence

Graph autoencoders (GAE) and variational graph autoencoders (VGAE) emerged as powerful methods for link prediction (LP). Their performances are less impressive on community detection (CD), where they are often outperformed by simpler alternatives such as the Louvain method. It is still unclear to what extent one can improve CD with GAE and VGAE, especially in the absence of node features. It is moreover uncertain whether one could do so while simultaneously preserving good performances on LP in a multi-task setting. In this workshop paper, summarizing results from our journal publication (Salha-Galvan et al. 2022), we show that jointly addressing these two tasks with high accuracy is possible. For this purpose, we introduce a community-preserving message passing scheme, doping our GAE and VGAE encoders by considering both the initial graph and Louvain-based prior communities when computing embedding spaces. Inspired by modularity-based clustering, we further propose novel training and optimization strategies specifically designed for joint LP and CD. We demonstrate the empirical effectiveness of our approach, referred to as Modularity-Aware GAE and VGAE, on various real-world graphs.


Can Strategic Data Collection Improve the Performance of Poverty Prediction Models?

arXiv.org Artificial Intelligence

Machine learning-based estimates of poverty and wealth are increasingly being used to guide the targeting of humanitarian aid and the allocation of social assistance. However, the ground truth labels used to train these models are typically borrowed from existing surveys that were designed to produce national statistics -- not to train machine learning models. Here, we test whether adaptive sampling strategies for ground truth data collection can improve the performance of poverty prediction models. Through simulations, we compare the status quo sampling strategies (uniform at random and stratified random sampling) to alternatives that prioritize acquiring training data based on model uncertainty or model performance on sub-populations. Perhaps surprisingly, we find that none of these active learning methods improve over uniform-at-random sampling. We discuss how these results can help shape future efforts to refine machine learning-based estimates of poverty.


Features for the 0-1 knapsack problem based on inclusionwise maximal solutions

arXiv.org Artificial Intelligence

Decades of research on the 0-1 knapsack problem led to very efficient algorithms that are able to quickly solve large problem instances to optimality. This prompted researchers to also investigate whether relatively small problem instances exist that are hard for existing solvers and investigate which features characterize their hardness. Previously the authors proposed a new class of hard 0-1 knapsack problem instances and demonstrated that the properties of so-called inclusionwise maximal solutions (IMSs) can be important hardness indicators for this class. In the current paper, we formulate several new computationally challenging problems related to the IMSs of arbitrary 0-1 knapsack problem instances. Based on generalizations of previous work and new structural results about IMSs, we formulate polynomial and pseudopolynomial time algorithms for solving these problems. From this we derive a set of 14 computationally expensive features, which we calculate for two large datasets on a supercomputer in approximately 540 CPU-hours. We show that the proposed features contain important information related to the empirical hardness of a problem instance that was missing in earlier features from the literature by training machine learning models that can accurately predict the empirical hardness of a wide variety of 0-1 knapsack problem instances. Using the instance space analysis methodology, we also show that hard 0-1 knapsack problem instances are clustered together around a relatively dense region of the instance space and several features behave differently in the easy and hard parts of the instance space.