Sailing in high-dimensional spaces: Low-dimensional embeddings through angle preservation

Low-dimensional embeddings (LDEs) of high-dimensional data are ubiquitous in science and engineering. They allow us to quickly understand the main properties of the data, identify outliers and processing errors, and inform the next steps of data analysis. As such, LDEs have to be faithful to the original high-dimensional data, i.e., they should represent the relationships that are encoded in the data, both at a local as well as global scale. The current generation of LDE approaches focus on reconstructing local distances between any pair of samples correctly, often out-performing traditional approaches aiming at all distances. For these approaches, global relationships are, however, usually strongly distorted, often argued to be an inherent trade-off between local and global structure learning for embeddings. We suggest a new perspective on LDE learning, reconstructing angles between data points. We show that this approach, Mercat, yields good reconstruction across a diverse set of experiments and metrics, and preserve structures well across all scales. Compared to existing work, our approach also has a simple formulation, facilitating future theoretical analysis and algorithmic improvements.

Not all tickets are equal and we know it: Guiding pruning with domain-specific knowledge

Neural structure learning is of paramount importance for scientific discovery and interpretability. Yet, contemporary pruning algorithms that focus on computational resource efficiency face algorithmic barriers to select a meaningful model that aligns with domain expertise. To mitigate this challenge, we propose DASH, which guides pruning by available domain-specific structural information. In the context of learning dynamic gene regulatory network models, we show that DASH combined with existing general knowledge on interaction partners provides data-specific insights aligned with biology. For this task, we show on synthetic data with ground truth information and two real world applications the effectiveness of DASH, which outperforms competing methods by a large margin and provides more meaningful biological insights. Our work shows that domain specific structural information bears the potential to improve model-derived scientific insights.

Finding Interpretable Class-Specific Patterns through Efficient Neural Search

Discovering patterns in data that best describe the differences between classes allows to hypothesize and reason about class-specific mechanisms. In molecular biology, for example, this bears promise of advancing the understanding of cellular processes differing between tissues or diseases, which could lead to novel treatments. To be useful in practice, methods that tackle the problem of finding such differential patterns have to be readily interpretable by domain experts, and scalable to the extremely high-dimensional data. In this work, we propose a novel, inherently interpretable binary neural network architecture DIFFNAPS that extracts differential patterns from data. DiffNaps is scalable to hundreds of thousands of features and robust to noise, thus overcoming the limitations of current state-of-the-art methods in large-scale applications such as in biology. We show on synthetic and real world data, including three biological applications, that, unlike its competitors, DiffNaps consistently yields accurate, succinct, and interpretable class descriptions

Understanding and Mitigating Classification Errors Through Interpretable Token Patterns

State-of-the-art NLP methods achieve human-like performance on many tasks, but make errors nevertheless. Characterizing these errors in easily interpretable terms gives insight into whether a classifier is prone to making systematic errors, but also gives a way to act and improve the classifier. We propose to discover those patterns of tokens that distinguish correct and erroneous predictions as to obtain global and interpretable descriptions for arbitrary NLP classifiers. We formulate the problem of finding a succinct and non-redundant set of such patterns in terms of the Minimum Description Length principle. Through an extensive set of experiments, we show that our method, Premise, performs well in practice. Unlike existing solutions, it recovers ground truth, even on highly imbalanced data over large vocabularies. In VQA and NER case studies, we confirm that it gives clear and actionable insight into the systematic errors made by NLP classifiers.

Preserving local densities in low-dimensional embeddings

Low-dimensional embeddings and visualizations are an indispensable tool for analysis of high-dimensional data. State-of-the-art methods, such as tSNE and UMAP, excel in unveiling local structures hidden in high-dimensional data and are therefore routinely applied in standard analysis pipelines in biology. We show, however, that these methods fail to reconstruct local properties, such as relative differences in densities (Fig. 1) and that apparent differences in cluster size can arise from computational artifact caused by differing sample sizes (Fig. 2). Providing a theoretical analysis of this issue, we then suggest dtSNE, which approximately conserves local densities. In an extensive study on synthetic benchmark and real world data comparing against five state-of-the-art methods, we empirically show that dtSNE provides similar global reconstruction, but yields much more accurate depictions of local distances and relative densities.

Plant 'n' Seek: Can You Find the Winning Ticket?

The lottery ticket hypothesis has sparked the rapid development of pruning algorithms that perform structure learning by identifying a sparse subnetwork of a large randomly initialized neural network. The existence of such 'winning tickets' has been proven theoretically but at suboptimal sparsity levels. Contemporary pruning algorithms have furthermore been struggling to identify sparse lottery tickets for complex learning tasks. Is this suboptimal sparsity merely an artifact of existence proofs and algorithms or a general limitation of the pruning approach? And, if very sparse tickets exist, are current algorithms able to find them or are further improvements needed to achieve effective network compression? To answer these questions systematically, we derive a framework to plant and hide target architectures within large randomly initialized neural networks. For three common challenges in machine learning, we hand-craft extremely sparse network topologies, plant them in large neural networks, and evaluate state-of-the-art lottery ticket pruning methods. We find that current limitations of pruning algorithms to identify extremely sparse tickets are likely of algorithmic rather than fundamental nature and anticipate that our planting framework will facilitate future developments of efficient pruning algorithms, as we have addressed the issue of missing baselines in the field raised by Frankle et al.

Federated Learning from Small Datasets

Federated learning allows multiple parties to collaboratively train a joint model without sharing local data. This enables applications of machine learning in settings of inherently distributed, undisclosable data such as in the medical domain. In practice, joint training is usually achieved by aggregating local models, for which local training objectives have to be in expectation similar to the joint (global) objective. Often, however, local datasets are so small that local objectives differ greatly from the global objective, resulting in federated learning to fail. We propose a novel approach that intertwines model aggregations with permutations of local models. The permutations expose each local model to a daisy chain of local datasets resulting in more efficient training in data-sparse domains. This enables training on extremely small local datasets, such as patient data across hospitals, while retaining the training efficiency and privacy benefits of federated learning.

Towards strong pruning for lottery tickets with non-zero biases

The strong lottery ticket hypothesis holds the promise that pruning randomly initialized deep neural networks could offer a computationally efficient alternative to deep learning with stochastic gradient descent. Common parameter initialization schemes and existence proofs, however, are focused on networks with zero biases, thus foregoing the potential universal approximation property of pruning. To fill this gap, we extend multiple initialization schemes and existence proofs to non-zero biases, including explicit 'looks-linear' approaches for ReLU activation functions. These do not only enable truly orthogonal parameter initialization but also reduce potential pruning errors. In experiments on standard benchmark data sets, we further highlight the practical benefits of non-zero bias initialization schemes, and present theoretically inspired extensions for state-of-the-art strong lottery ticket pruning.

Label-Descriptive Patterns and their Application to Characterizing Classification Errors

State-of-the-art deep learning methods achieve human-like performance on many tasks, but make errors nevertheless. Characterizing these errors in easily interpretable terms gives insight into whether a model is prone to making systematic errors, but also gives a way to act and improve the model. In this paper we propose a method that allows us to do so for arbitrary classifiers by mining a small set of patterns that together succinctly describe the input data that is partitioned according to correctness of prediction. We show this is an instance of the more general label description problem, which we formulate in terms of the Minimum Description Length principle. To discover good pattern sets we propose the efficient and hyperparameter-free Premise algorithm, which through an extensive set of experiments we show on both synthetic and real-world data performs very well in practice; unlike existing solutions it ably recovers ground truth patterns, even on highly imbalanced data over many unique items, or where patterns are only weakly associated to labels. Through two real-world case studies we confirm that Premise gives clear and actionable insight into the systematic errors made by modern NLP classifiers.

Factoring out prior knowledge from low-dimensional embeddings

Low-dimensional embedding techniques such as tSNE and UMAP allow visualizing high-dimensional data and therewith facilitate the discovery of interesting structure. Although they are widely used, they visualize data as is, rather than in light of the background knowledge we have about the data. What we already know, however, strongly determines what is novel and hence interesting. In this paper we propose two methods for factoring out prior knowledge in the form of distance matrices from low-dimensional embeddings. To factor out prior knowledge from tSNE embeddings, we propose JEDI that adapts the tSNE objective in a principled way using Jensen-Shannon divergence. To factor out prior knowledge from any downstream embedding approach, we propose CONFETTI, in which we directly operate on the input distance matrices. Extensive experiments on both synthetic and real world data show that both methods work well, providing embeddings that exhibit meaningful structure that would otherwise remain hidden.