Peter Tino

Sreejita Ghosh, Elizabeth S. Baranowski, Michael Biehl et al.

Application of interpretable machine learning techniques on medical datasets facilitate early and fast diagnoses, along with getting deeper insight into the data. Furthermore, the transparency of these models increase trust among application domain experts. Medical datasets face common issues such as heterogeneous measurements, imbalanced classes with limited sample size, and missing data, which hinder the straightforward application of machine learning techniques. In this paper we present a family of prototype-based (PB) interpretable models which are capable of handling these issues. The models introduced in this contribution show comparable or superior performance to alternative techniques applicable in such situations. However, unlike ensemble based models, which have to compromise on easy interpretation, the PB models here do not. Moreover we propose a strategy of harnessing the power of ensembles while maintaining the intrinsic interpretability of the PB models, by averaging the model parameter manifolds. All the models were evaluated on a synthetic (publicly available dataset) in addition to detailed analyses of two real-world medical datasets (one publicly available). Results indicated that the models and strategies we introduced addressed the challenges of real-world medical data, while remaining computationally inexpensive and transparent, as well as similar or superior in performance compared to their alternatives.

Shanshan Mao, Peter Tino

A central premise in evolutionary biology is that individual variation can generate information asymmetries that facilitate the emergence of hierarchical organisation. To examine this process, we develop an agent-based model (ABM) to identify the minimal conditions under which hierarchy arises in dynamic multi-agent systems, focusing on the roles of initial heterogeneity and mutation amplitude across generations. Hierarchical organisation is quantified using the Trophic Incoherence (TI) metric, which captures directional asymmetries in interaction networks. Our results show that even small individual differences can be amplified through repeated local interactions involving reproduction, competition, and cooperation, but that hierarchical order is markedly more sensitive to mutation amplitude than to initial heterogeneity. Across repeated trials, stable hierarchies reliably emerge only when mutation amplitude is sufficiently high, while initial heterogeneity primarily affects early formation rather than long-term persistence. Overall, these findings demonstrate how simple interaction rules can give rise to both the emergence and persistence of hierarchical organisation, providing a quantitative account of how structured inequality can develop from initially homogeneous populations.

Tamsin James, Ben Williamson, Peter Tino et al.

How can we identify causal genetic mechanisms that govern bacterial traits? Initial efforts entrusting machine learning models to handle the task of predicting phenotype from genotype return high accuracy scores. However, attempts to extract any meaning from the predictive models are found to be corrupted by falsely identified "causal" features. Relying solely on pattern recognition and correlations is unreliable, significantly so in bacterial genomics settings where high-dimensionality and spurious associations are the norm. Though it is not yet clear whether we can overcome this hurdle, significant efforts are being made towards discovering potential high-risk bacterial genetic variants. In view of this, we set up open problems surrounding phenotype prediction from bacterial whole-genome datasets and extending those to learning causal effects, and discuss challenges that impact the reliability of a machine's decision-making when faced with datasets of this nature.

Peter Tino, Robert Simon Fong, Roberto Fabio Leonarduzzi

This work proposes a time series prediction method based on the kernel view of linear reservoirs. In particular, the time series motifs of the reservoir kernel are used as representational basis on which general readouts are constructed. We provide a geometric interpretation of our approach shedding light on how our approach is related to the core reservoir models and in what way the two approaches differ. Empirical experiments then compare predictive performances of our suggested model with those of recent state-of-art transformer based models, as well as the established recurrent network model - LSTM. The experiments are performed on both univariate and multivariate time series and with a variety of prediction horizons. Rather surprisingly we show that even when linear readout is employed, our method has the capacity to outperform transformer models on univariate time series and attain competitive results on multivariate benchmark datasets. We conclude that simple models with easily controllable capacity but capturing enough memory and subsequence structure can outperform potentially over-complicated deep learning models. This does not mean that reservoir motif based models are preferable to other more complex alternatives - rather, when introducing a new complex time series model one should employ as a sanity check simple, but potentially powerful alternatives/baselines such as reservoir models or the models introduced here.

Janis Norden, Elisa Oostwal, Michael Chappell et al.

The successful application of modern machine learning for time series classification is often hampered by limitations in quality and quantity of available training data. To overcome these limitations, available domain expert knowledge in the form of parametrised mechanistic dynamical models can be used whenever it is available and time series observations may be represented as an element from a given class of parametrised dynamical models. This makes the learning process interpretable and allows the modeller to deal with sparsely and irregularly sampled data in a natural way. However, the internal processes of a dynamical model are often only partially observed. This can lead to ambiguity regarding which particular model realization best explains a given time series observation. This problem is well-known in the literature, and a dynamical model with this issue is referred to as structurally unidentifiable. Training a classifier that incorporates knowledge about a structurally unidentifiable dynamical model can negatively influence classification performance. To address this issue, we employ structural identifiability analysis to explicitly relate parameter configurations that are associated with identical system outputs. Using the derived relations in classifier training, we demonstrate that this method significantly improves the classifier's ability to generalize to unseen data on a number of example models from the biomedical domain. This effect is especially pronounced when the number of training instances is limited. Our results demonstrate the importance of accounting for structural identifiability, a topic that has received relatively little attention from the machine learning community.

Marco Canducci, Lida Abdi, Alessandro Prete et al.

In a given classification task, the accuracy of the learner is often hampered by finiteness of the training set, high-dimensionality of the feature space and severe overlap between classes. In the context of interpretable learners, with (piecewise) linear separation boundaries, these issues can be mitigated by careful construction of optimization procedures and/or estimation of relevant features for the task. However, when the task is shared across two disjoint populations the main interest is shifted towards estimating a set of features that discriminate the most between the two, when performing classification. We propose a new Discriminative Subspace Emersion (DSE) method to extend subspace learning toward a general relevance learning framework. DSE allows us to identify the most relevant features in distinguishing the classification task across two populations, even in cases of high overlap between classes. The proposed methodology is designed to work with multiple sets of labels and is derived in principle without being tied to a specific choice of base learner. Theoretical and empirical investigations over synthetic and real-world datasets indicate that DSE accurately identifies a common subspace for the classification across different populations. This is shown to be true for a surprisingly high degree of overlap between classes.

Antony R. Lee, Peter Tino, Iain Bruce Styles

Motivated by information geometry, a distance function on the space of stochastic matrices is advocated. Starting with sequences of Markov chains the Bhattacharyya angle is advocated as the natural tool for comparing both short and long term Markov chain runs. Bounds on the convergence of the distance and mixing times are derived. Guided by the desire to compare different Markov chain models, especially in the setting of healthcare processes, a new distance function on the space of stochastic matrices is presented. It is a true distance measure which has a closed form and is efficient to implement for numerical evaluation. In the case of ergodic Markov chains, it is shown that considering either the Bhattacharyya angle on Markov sequences or the new stochastic matrix distance leads to the same distance between models.

Giuseppe Serra, Peter Tino, Zhao Xu et al.

Nowadays, neural network (NN) and deep learning (DL) techniques are widely adopted in many applications, including recommender systems. Given the sparse and stochastic nature of collaborative filtering (CF) data, recent works have critically analyzed the effective improvement of neural-based approaches compared to simpler and often transparent algorithms for recommendation. Previous results showed that NN and DL models can be outperformed by traditional algorithms in many tasks. Moreover, given the largely black-box nature of neural-based methods, interpretable results are not naturally obtained. Following on this debate, we first present a transparent probabilistic model that topologically organizes user and product latent classes based on the review information. In contrast to popular neural techniques for representation learning, we readily obtain a statistical, visualization-friendly tool that can be easily inspected to understand user and product characteristics from a textual-based perspective. Then, given the limitations of common embedding techniques, we investigate the possibility of using the estimated interpretable quantities as model input for a rating prediction task. To contribute to the recent debates, we evaluate our results in terms of both capacity for interpretability and predictive performances in comparison with popular text-based neural approaches. The results demonstrate that the proposed latent class representations can yield competitive predictive performances, compared to popular, but difficult-to-interpret approaches.

Fengzhen Tang, Haifeng Feng, Peter Tino et al.

In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive definite matrices, which are inherently points that live on a curved Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, traditional Euclidean machine learning algorithms yield poor results on such data. In this paper, we generalize the probabilistic learning vector quantization algorithm for data points living on the manifold of symmetric positive definite matrices equipped with Riemannian natural metric (affine-invariant metric). By exploiting the induced Riemannian distance, we derive the probabilistic learning Riemannian space quantization algorithm, obtaining the learning rule through Riemannian gradient descent. Empirical investigations on synthetic data, image data , and motor imagery EEG data demonstrate the superior performance of the proposed method.

Tom Goodman, Karoline van Gemst, Peter Tino

This paper presents a geometric approach to pitch estimation (PE)-an important problem in Music Information Retrieval (MIR), and a precursor to a variety of other problems in the field. Though there exist a number of highly-accurate methods, both mono-pitch estimation and multi-pitch estimation (particularly with unspecified polyphonic timbre) prove computationally and conceptually challenging. A number of current techniques, whilst incredibly effective, are not targeted towards eliciting the underlying mathematical structures that underpin the complex musical patterns exhibited by acoustic musical signals. Tackling the approach from both a theoretical and experimental perspective, we present a novel framework, a basis for further work in the area, and results that (whilst not state of the art) demonstrate relative efficacy. The framework presented in this paper opens up a completely new way to tackle PE problems, and may have uses both in traditional analytical approaches, as well as in the emerging machine learning (ML) methods that currently dominate the literature.

Abolfazl Taghribi, Kerstin Bunte, Rory Smith et al.

Dimensionality reduction and clustering are often used as preliminary steps for many complex machine learning tasks. The presence of noise and outliers can deteriorate the performance of such preprocessing and therefore impair the subsequent analysis tremendously. In manifold learning, several studies indicate solutions for removing background noise or noise close to the structure when the density is substantially higher than that exhibited by the noise. However, in many applications, including astronomical datasets, the density varies alongside manifolds that are buried in a noisy background. We propose a novel method to extract manifolds in the presence of noise based on the idea of Ant colony optimization. In contrast to the existing random walk solutions, our technique captures points that are locally aligned with major directions of the manifold. Moreover, we empirically show that the biologically inspired formulation of ant pheromone reinforces this behavior enabling it to recover multiple manifolds embedded in extremely noisy data clouds. The algorithm performance in comparison to state-of-the-art approaches for noise reduction in manifold detection and clustering is demonstrated, on several synthetic and real datasets, including an N-body simulation of a cosmological volume.

Sreejita Ghosh, Peter Tino, Kerstin Bunte

Increasing number of sectors which affect human lives, are using Machine Learning (ML) tools. Hence the need for understanding their working mechanism and evaluating their fairness in decision-making, are becoming paramount, ushering in the era of Explainable AI (XAI). In this contribution we introduced a few intrinsically interpretable models which are also capable of dealing with missing values, in addition to extracting knowledge from the dataset and about the problem. These models are also capable of visualisation of the classifier and decision boundaries: they are the angle based variants of Learning Vector Quantization. We have demonstrated the algorithms on a synthetic dataset and a real-world one (heart disease dataset from the UCI repository). The newly developed classifiers helped in investigating the complexities of the UCI dataset as a multiclass problem. The performance of the developed classifiers were comparable to those reported in literature for this dataset, with additional value of interpretability, when the dataset was treated as a binary class problem.

Pietro Verzelli, Cesare Alippi, Lorenzo Livi et al.

Reservoir computing is a popular approach to design recurrent neural networks, due to its training simplicity and approximation performance. The recurrent part of these networks is not trained (e.g., via gradient descent), making them appealing for analytical studies by a large community of researchers with backgrounds spanning from dynamical systems to neuroscience. However, even in the simple linear case, the working principle of these networks is not fully understood and their design is usually driven by heuristics. A novel analysis of the dynamics of such networks is proposed, which allows the investigator to express the state evolution using the controllability matrix. Such a matrix encodes salient characteristics of the network dynamics; in particular, its rank represents an input-indepedent measure of the memory capacity of the network. Using the proposed approach, it is possible to compare different reservoir architectures and explain why a cyclic topology achieves favourable results as verified by practitioners.

Lukas Pfannschmidt, Jonathan Jakob, Fabian Hinder et al.

Advances in machine learning technologies have led to increasingly powerful models in particular in the context of big data. Yet, many application scenarios demand for robustly interpretable models rather than optimum model accuracy; as an example, this is the case if potential biomarkers or causal factors should be discovered based on a set of given measurements. In this contribution, we focus on feature selection paradigms, which enable us to uncover relevant factors of a given regularity based on a sparse model. We focus on the important specific setting of linear ordinal regression, i.e.\ data have to be ranked into one of a finite number of ordered categories by a linear projection. Unlike previous work, we consider the case that features are potentially redundant, such that no unique minimum set of relevant features exists. We aim for an identification of all strongly and all weakly relevant features as well as their type of relevance (strong or weak); we achieve this goal by determining feature relevance bounds, which correspond to the minimum and maximum feature relevance, respectively, if searched over all equivalent models. In addition, we discuss how this setting enables us to substitute some of the features, e.g.\ due to their semantics, and how to extend the framework of feature relevance intervals to the setting of privileged information, i.e.\ potentially relevant information is available for training purposes only, but cannot be used for the prediction itself.

Peter Tino

Parameterized state space models in the form of recurrent networks are often used in machine learning to learn from data streams exhibiting temporal dependencies. To break the black box nature of such models it is important to understand the dynamical features of the input driving time series that are formed in the state space. We propose a framework for rigorous analysis of such state representations in vanishing memory state space models such as echo state networks (ESN). In particular, we consider the state space a temporal feature space and the readout mapping from the state space a kernel machine operating in that feature space. We show that: (1) The usual ESN strategy of randomly generating input-to-state, as well as state coupling leads to shallow memory time series representations, corresponding to cross-correlation operator with fast exponentially decaying coefficients; (2) Imposing symmetry on dynamic coupling yields a constrained dynamic kernel matching the input time series with straightforward exponentially decaying motifs or exponentially decaying motifs of the highest frequency; (3) Simple cycle high-dimensional reservoir topology specified only through two free parameters can implement deep memory dynamic kernels with a rich variety of matching motifs. We quantify richness of feature representations imposed by dynamic kernels and demonstrate that for dynamic kernel associated with cycle reservoir topology, the kernel richness undergoes a phase transition close to the edge of stability.

Maria Perez-Ortiz, Peter Tino, Rafal Mantiuk et al.

Data augmentation is rapidly gaining attention in machine learning. Synthetic data can be generated by simple transformations or through the data distribution. In the latter case, the main challenge is to estimate the label associated to new synthetic patterns. This paper studies the effect of generating synthetic data by convex combination of patterns and the use of these as unsupervised information in a semi-supervised learning framework with support vector machines, avoiding thus the need to label synthetic examples. We perform experiments on a total of 53 binary classification datasets. Our results show that this type of data over-sampling supports the well-known cluster assumption in semi-supervised learning, showing outstanding results for small high-dimensional datasets and imbalanced learning problems.

Maria Perez-Ortiz, Pedro A. Gutierrez, Peter Tino et al.

Weather and atmospheric patterns are often persistent. The simplest weather forecasting method is the so-called persistence model, which assumes that the future state of a system will be similar (or equal) to the present state. Machine learning (ML) models are widely used in different weather forecasting applications, but they need to be compared to the persistence model to analyse whether they provide a competitive solution to the problem at hand. In this paper, we devise a new model for predicting low-visibility in airports using the concepts of mixture of experts. Visibility level is coded as two different ordered categorical variables: cloud height and runway visual height. The underlying system in this application is stagnant approximately in 90% of the cases, and standard ML models fail to improve on the performance of the persistence model. Because of this, instead of trying to simply beat the persistence model using ML, we use this persistence as a baseline and learn an ordinal neural network model that refines its results by focusing on learning weather fluctuations. The results show that the proposal outperforms persistence and other ordinal autoregressive models, especially for longer time horizon predictions and for the runway visual height variable.

Lukas Pfannschmidt, Jonathan Jakob, Michael Biehl et al.

The increasing occurrence of ordinal data, mainly sociodemographic, led to a renewed research interest in ordinal regression, i.e. the prediction of ordered classes. Besides model accuracy, the interpretation of these models itself is of high relevance, and existing approaches therefore enforce e.g. model sparsity. For high dimensional or highly correlated data, however, this might be misleading due to strong variable dependencies. In this contribution, we aim for an identification of feature relevance bounds which - besides identifying all relevant features - explicitly differentiates between strongly and weakly relevant features.

Fani Tsapeli, Peter Tino, Mirco Musolesi

The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal inference studies may require unobserved high-level information which needs to be inferred from other observed attributes. In such cases, inaccuracies of the applied inference methods will result in noisy outputs. In this study, we propose a novel approach for causal inference when one or more key variables are noisy. Our method utilizes the knowledge about the uncertainty of the real values of key variables in order to reduce the bias induced by noisy measurements. We evaluate our approach in comparison with existing methods both on simulated and real scenarios and we demonstrate that our method reduces the bias and avoids false causal inference conclusions in most cases.

Yuan Shen, Peter Tino, Krasimira Tsaneva-Atanasova

We present a general framework for classifying partially observed dynamical systems based on the idea of learning in the model space. In contrast to the existing approaches using model point estimates to represent individual data items, we employ posterior distributions over models, thus taking into account in a principled manner the uncertainty due to both the generative (observational and/or dynamic noise) and observation (sampling in time) processes. We evaluate the framework on two testbeds - a biological pathway model and a stochastic double-well system. Crucially, we show that the classifier performance is not impaired when the model class used for inferring posterior distributions is much more simple than the observation-generating model class, provided the reduced complexity inferential model class captures the essential characteristics needed for the given classification task.

Frank-Michael Schleif, Andrej Gisbrecht, Peter Tino

Indefinite similarity measures can be frequently found in bio-informatics by means of alignment scores, but are also common in other fields like shape measures in image retrieval. Lacking an underlying vector space, the data are given as pairwise similarities only. The few algorithms available for such data do not scale to larger datasets. Focusing on probabilistic batch classifiers, the Indefinite Kernel Fisher Discriminant (iKFD) and the Probabilistic Classification Vector Machine (PCVM) are both effective algorithms for this type of data but, with cubic complexity. Here we propose an extension of iKFD and PCVM such that linear runtime and memory complexity is achieved for low rank indefinite kernels. Employing the Nyström approximation for indefinite kernels, we also propose a new almost parameter free approach to identify the landmarks, restricted to a supervised learning problem. Evaluations at several larger similarity data from various domains show that the proposed methods provides similar generalization capabilities while being easier to parametrize and substantially faster for large scale data.

Nikolaos Gianniotis, Dennis Kügler, Peter Tino et al.

We present an algorithm for the visualisation of time series. To that end we employ echo state networks to convert time series into a suitable vector representation which is capable of capturing the latent dynamics of the time series. Subsequently, the obtained vector representations are put through an autoencoder and the visualisation is constructed using the activations of the bottleneck. The crux of the work lies with defining an objective function that quantifies the reconstruction error of these representations in a principled manner. We demonstrate the method on synthetic and real data.

Huanhuan Chen, Peter Tino, Xin Yao et al.

The emergence of large scaled sensor networks facilitates the collection of large amounts of real-time data to monitor and control complex engineering systems. However, in many cases the collected data may be incomplete or inconsistent, while the underlying environment may be time-varying or un-formulated. In this paper, we have developed an innovative cognitive fault diagnosis framework that tackles the above challenges. This framework investigates fault diagnosis in the model space instead of in the signal space. Learning in the model space is implemented by fitting a series of models using a series of signal segments selected with a rolling window. By investigating the learning techniques in the fitted model space, faulty models can be discriminated from healthy models using one-class learning algorithm. The framework enables us to construct fault library when unknown faults occur, which can be regarded as cognitive fault isolation. This paper also theoretically investigates how to measure the pairwise distance between two models in the model space and incorporates the model distance into the learning algorithm in the model space. The results on three benchmark applications and one simulated model for the Barcelona water distribution network have confirmed the effectiveness of the proposed framework.