Order is one of the main instruments to measure the relationship between objects in (empirical) data. However, compared to methods that use numerical properties of objects, the amount of ordinal methods developed is rather small. One reason for this is the limited availability of computational resources in the last century that would have been required for ordinal computations. Another reason -- particularly important for this line of research -- is that order-based methods are often seen as too mathematically rigorous for applying them to real-world data. In this paper, we will therefore discuss different means for measuring and 'calculating' with ordinal structures -- a specific class of directed graphs -- and show how to infer knowledge from them. Our aim is to establish Ordinal Data Science as a fundamentally new research agenda. Besides cross-fertilization with other cornerstone machine learning and knowledge representation methods, a broad range of disciplines will benefit from this endeavor, including, psychology, sociology, economics, web science, knowledge engineering, scientometrics.

Hyperbolic geometry has recently garnered considerable attention in machine learning due to its capacity to embed hierarchical graph structures with low distortions for further downstream processing. This paper introduces a simple framework to detect local outliers for datasets grounded in hyperbolic 2-space referred to as HLoOP (Hyperbolic Local Outlier Probability). Within a Euclidean space, well-known techniques for local outlier detection are based on the Local Outlier Factor (LOF) and its variant, the LoOP (Local Outlier Probability), which incorporates probabilistic concepts to model the outlier level of a data vector. The developed HLoOP combines the idea of finding nearest neighbors, density-based outlier scoring with a probabilistic, statistically oriented approach. Therefore, the method consists in computing the Riemmanian distance of a data point to its nearest neighbors following a Gaussian probability density function expressed in a hyperbolic space. This is achieved by defining a Gaussian cumulative distribution in this space. The HLoOP algorithm is tested on the WordNet dataset yielding promising results. Code and data will be made available on request for reproductibility.

This paper introduces GeoShapley, a game theory approach to measuring spatial effects in machine learning models. GeoShapley extends the Nobel Prize-winning Shapley value framework in game theory by conceptualizing location as a player in a model prediction game, which enables the quantification of the importance of location and the synergies between location and other features in a model. GeoShapley is a model-agnostic approach and can be applied to statistical or black-box machine learning models in various structures. The interpretation of GeoShapley is directly linked with spatially varying coefficient models for explaining spatial effects and additive models for explaining non-spatial effects. Using simulated data, GeoShapley values are validated against known data-generating processes and are used for cross-comparison of seven statistical and machine learning models. An empirical example of house price modeling is used to illustrate GeoShapley's utility and interpretation with real world data. The method is available as an open-source Python package named geoshapley.

Speech, language, and communication deficits are present in most neurodegenerative syndromes. They enable the early detection, diagnosis, treatment planning, and monitoring of neurocognitive disease progression as part of traditional neurological assessment. Nevertheless, standard speech and language evaluation is time-consuming and resource-intensive for clinicians. We argue that using machine learning methodologies, natural language processing, and modern artificial intelligence (AI) for Language Assessment is an improvement over conventional manual assessment. Using these methodologies, Computational Language Assessment (CLA) accomplishes three goals: (i) provides a neuro-cognitive evaluation of speech, language, and communication in elderly and high-risk individuals for dementia; (ii) facilitates the diagnosis, prognosis, and therapy efficacy in at-risk and language-impaired populations; and (iii) allows easier extensibility to assess patients from a wide range of languages. By employing AI models, CLA may inform neurocognitive theory on the relationship between language symptoms and their neural bases. Finally, it signals a paradigm shift by significantly advancing our ability to optimize the prevention and treatment of elderly individuals with communication disorders, allowing them to age gracefully with social engagement.

Near-infrared spectroscopy (NIRS) can measure neural activity through blood oxygenation changes in the brain in a wearable form factor, enabling unique applications for research in and outside the lab. NIRS has proven capable of measuring cognitive states such as mental workload, often using machine learning (ML) based brain-computer interfaces (BCIs). To date, NIRS research has largely relied on probes with under ten to several hundred channels, although recently a new class of wearable NIRS devices with thousands of channels has emerged. This poses unique challenges for ML classification, as NIRS is typically limited by few training trials which results in severely under-determined estimation problems. So far, it is not well understood how such high-resolution data is best leveraged in practical BCIs and whether state-of-the-art (SotA) or better performance can be achieved. To address these questions, we propose an ML strategy to classify working-memory load that relies on spatio-temporal regularization and transfer learning from other subjects in a combination that has not been used in previous NIRS BCIs. The approach can be interpreted as an end-to-end generalized linear model and allows for a high degree of interpretability using channel-level or cortical imaging approaches. We show that using the proposed methodology, it is possible to achieve SotA decoding performance with high-resolution NIRS data. We also replicated several SotA approaches on our dataset of 43 participants wearing a 3198 dual-channel NIRS device while performing the n-Back task and show that these existing methods struggle in the high-channel regime and are largely outperformed by the proposed method. Our approach helps establish high-channel NIRS devices as a viable platform for SotA BCI and opens new applications using this class of headset while also enabling high-resolution model imaging and interpretation.

In this paper, we study the method to reconstruct dynamical systems from data without time labels. Data without time labels appear in many applications, such as molecular dynamics, single-cell RNA sequencing etc. Reconstruction of dynamical system from time sequence data has been studied extensively. However, these methods do not apply if time labels are unknown. Without time labels, sequence data becomes distribution data. Based on this observation, we propose to treat the data as samples from a probability distribution and try to reconstruct the underlying dynamical system by minimizing the distribution loss, sliced Wasserstein distance more specifically. Extensive experiment results demonstrate the effectiveness of the proposed method.

Face clustering tasks can learn hierarchical semantic information from large-scale data, which has the potential to help facilitate face recognition. However, there are few works on this problem. This paper explores it by proposing a joint optimization task of label classification and supervised contrastive clustering to introduce the cluster knowledge to the traditional face recognition task in two ways. We first extend ArcFace with a cluster-guided angular margin to adjust the within-class feature distribution according to the hard level of face clustering. Secondly, we propose a supervised contrastive clustering approach to pull the features to the cluster center and propose the cluster-aligning procedure to align the cluster center and the learnable class center in the classifier for joint training. Finally, extensive qualitative and quantitative experiments on popular facial benchmarks demonstrate the effectiveness of our paradigm and its superiority over the existing approaches to face recognition.

Joint embedding (JE) architectures have emerged as a promising avenue for acquiring transferable data representations. A key obstacle to using JE methods, however, is the inherent challenge of evaluating learned representations without access to a downstream task, and an annotated dataset. Without efficient and reliable evaluation, it is difficult to iterate on architectural and training choices for JE methods. In this paper, we introduce LiDAR (Linear Discriminant Analysis Rank), a metric designed to measure the quality of representations within JE architectures. Our metric addresses several shortcomings of recent approaches based on feature covariance rank by discriminating between informative and uninformative features. In essence, LiDAR quantifies the rank of the Linear Discriminant Analysis (LDA) matrix associated with the surrogate SSL task -- a measure that intuitively captures the information content as it pertains to solving the SSL task. We empirically demonstrate that LiDAR significantly surpasses naive rank based approaches in its predictive power of optimal hyperparameters. Our proposed criterion presents a more robust and intuitive means of assessing the quality of representations within JE architectures, which we hope facilitates broader adoption of these powerful techniques in various domains.

Due to the availability of only a few labeled instances for the novel target prediction task and the significant domain shift between the well annotated source domain and the target domain, cross-domain few-shot learning (CDFSL) induces a very challenging adaptation problem. In this paper, we propose a simple Adaptive Weighted Co-Learning (AWCoL) method to address the CDFSL challenge by adapting two independently trained source prototypical classification models to the target task in a weighted co-learning manner. The proposed method deploys a weighted moving average prediction strategy to generate probabilistic predictions from each model, and then conducts adaptive co-learning by jointly fine-tuning the two models in an alternating manner based on the pseudo-labels and instance weights produced from the predictions. Moreover, a negative pseudo-labeling regularizer is further deployed to improve the fine-tuning process by penalizing false predictions. Comprehensive experiments are conducted on multiple benchmark datasets and the empirical results demonstrate that the proposed method produces state-of-the-art CDFSL performance.

Zipf (1935) posited that wordforms are optimized to minimize utterances' communicative costs. Under the assumption that cost is given by an utterance's length, he supported this claim by showing that words' lengths are inversely correlated with their frequencies. Communicative cost, however, can be operationalized in different ways. Piantadosi et al. (2011) claim that cost should be measured as the distance between an utterance's information rate and channel capacity, which we dub the channel capacity hypothesis (CCH) here. Following this logic, they then proposed that a word's length should be proportional to the expected value of its surprisal (negative log-probability in context). In this work, we show that Piantadosi et al.'s derivation does not minimize CCH's cost, but rather a lower bound, which we term CCH-lower. We propose a novel derivation, suggesting an improved way to minimize CCH's cost. Under this method, we find that a language's word lengths should instead be proportional to the surprisal's expectation plus its variance-to-mean ratio. Experimentally, we compare these three communicative cost functions: Zipf's, CCH-lower , and CCH. Across 13 languages and several experimental settings, we find that length is better predicted by frequency than either of the other hypotheses. In fact, when surprisal's expectation, or expectation plus variance-to-mean ratio, is estimated using better language models, it leads to worse word length predictions. We take these results as evidence that Zipf's longstanding hypothesis holds.