Identifying the potential oligogenic causes of rare diseases remains a challenge, notwithstanding the advancements made in the last decade. While a variety of predictive and ranking approaches have been proposed, their precision remains limited, as only a small number of high-quality training cases are available and it remains difficult to know which features may be most relevant for the design of new predictors. We hypothesize here that structured biological information, which provides an integration of various relevant biological networks and ontologies in a single heterogeneous knowledge graph, can make a difference as it allows for learning a relevant genetic representation through KGE methods. An exhaustive benchmarking is performed here wherein we assess the performance of various state-of-the-art embedding models for the task of identifying potentially pathogenic gene pairs. The results obtained show that these KGE provide highly accurate predictions, leading to an Area Under the Precision-Recall Curve of up to $0.93$, representing also a significant advancement over previous approaches for predicting gene pairs involved in oligogenic diseases. We show nonetheless that care needs to be taken in the cross-validation when using embeddings, as data leakage between folds in embedding space will reveal overly optimistic results. The further evaluation of the methods on a holdout set as well as on a group of new male infertility cases show that three Translational Distance models (TransE, MurE, and RotatE) and two of the Semantic Matching models (DisMult and QuatE) provide the better results. The analysis is concluded by comparing all known gene combinations for these top-ranking models, examining their similarities and differences. Overall, KGE provide a predictive advancement but new steps will need to be taken generate explanations as to why the pairs are relevant for oligogenic diseases.

The Modified Cramér-Rao Bound (MCRB) proves to be of significant importance in non-standard estimation scenarios, when in addition to unknown deterministic parameters to be estimated, observations also depend on random nuisance parameters. Given the interest of applications that involve estimation on Lie Groups (LGs), as well as the relevance of nonstandard estimation problems in many practical scenarios, the main concern in this communication is to derive an intrinsic MCRB on LGs (LG-MCRB). For this purpose, a modified unbiasedness constraint must be defined, yielding a modified Barankin Bound. A closed-form formula of the LG-MCRB is then provided for a LG Gaussian model on $S O(2)$, representing $2 D$ rotation matrices, while considering non-Gaussian random nuisance parameters. The validity of this expression is then assessed through numerical simulations, and compared with the intrinsic CRB on LGs for a simplified illustrative scenario, involving a concentrated Gaussian prior distribution on the random nuisance parameters.

MOTIVATION: Whole exome sequencing (WES) has emerged as a powerful tool for genetic research, enabling the collection of a tremendous amount of data about human genetic variation. However, properly identifying which variants are causative of a genetic disease remains an important challenge, often due to the number of variants that need to be screened. Expanding the screening to combinations of variants in two or more genes, as would be required under the oligogenic inheritance model, simply blows this problem out of proportion. RESULTS: We present here the High-throughput oligogenic prioritizer (Hop), a novel prioritization method that uses direct oligogenic information at the variant, gene and gene pair level to detect digenic variant combinations in WES data. This method leverages information from a knowledge graph, together with specialized pathogenicity predictions in order to effectively rank variant combinations based on how likely they are to explain the patient's phenotype. The performance of Hop is evaluated in cross-validation on 36 120 synthetic exomes for training and 14 280 additional synthetic exomes for independent testing. Whereas the known pathogenic variant combinations are found in the top 20 in approximately 60% of the cross-validation exomes, 71% are found in the same ranking range when considering the independent set. These results provide a significant improvement over alternative approaches that depend simply on a monogenic assessment of pathogenicity, including early attempts for digenic ranking using monogenic pathogenicity scores. AVAILABILITY AND IMPLEMENTATION: Hop is available at https://github.com/oligogenic/HOP.

This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup, the chosen Riemannian metric induces a geometry for the parameter manifold, as well as an intrinsic notion of the estimation error measure. Performance bounds for such error measure were previously obtained in the non-Bayesian case (when the unknown parameter is assumed to deterministic), and referred to as intrinsic Cramér-Rao bound. The presented result then appears either as: a) an extension of the intrinsic Cramér-Rao bound to the Bayesian estimation framework; b) a generalization of the Van-Trees inequality (Bayesian Cramér-Rao bound) that accounts for the aforementioned geometric structures. In a second part, we leverage this formalism to study the problem of covariance matrix estimation when the data follow a Gaussian distribution, and whose covariance matrix is drawn from an inverse Wishart distribution. Performance bounds for this problem are obtained for both the mean squared error (Euclidean metric) and the natural Riemannian distance for Hermitian positive definite matrices (affine invariant metric). Numerical simulation illustrate that assessing the error with the affine invariant metric is revealing of interesting properties of the maximum a posteriori and minimum mean square error estimator, which are not observed when using the Euclidean metric.

In this communication, we derive a new intrinsic Cramér-Rao bound for both parameters and observations lying on Lie groups. The expression is obtained by using the intrinsic properties of Lie groups. An exact expression is obtained for the case where parameters and observations are in SE(2), the semi-direct Lie group of 2D rotation and 2D translation. To support the discussion, the proposed bound is numerically validated for a Lie group Gaussian model on SE(2).

BACKGROUND: Understanding the impact of gene interactions on disease phenotypes is increasingly recognised as a crucial aspect of genetic disease research. This trend is reflected by the growing amount of clinical research on oligogenic diseases, where disease manifestations are influenced by combinations of variants on a few specific genes. Although statistical machine-learning methods have been developed to identify relevant genetic variant or gene combinations associated with oligogenic diseases, they rely on abstract features and black-box models, posing challenges to interpretability for medical experts and impeding their ability to comprehend and validate predictions. In this work, we present a novel, interpretable predictive approach based on a knowledge graph that not only provides accurate predictions of disease-causing gene interactions but also offers explanations for these results. RESULTS: We introduce BOCK, a knowledge graph constructed to explore disease-causing genetic interactions, integrating curated information on oligogenic diseases from clinical cases with relevant biomedical networks and ontologies. Using this graph, we developed a novel predictive framework based on heterogenous paths connecting gene pairs. This method trains an interpretable decision set model that not only accurately predicts pathogenic gene interactions, but also unveils the patterns associated with these diseases. A unique aspect of our approach is its ability to offer, along with each positive prediction, explanations in the form of subgraphs, revealing the specific entities and relationships that led to each pathogenic prediction. CONCLUSION: Our method, built with interpretability in mind, leverages heterogenous path information in knowledge graphs to predict pathogenic gene interactions and generate meaningful explanations. This not only broadens our understanding of the molecular mechanisms underlying oligogenic diseases, but also presents a novel application of knowledge graphs in creating more transparent and insightful predictors for genetic research.

BACKGROUND: The prediction of potentially pathogenic variant combinations in patients remains a key task in the field of medical genetics for the understanding and detection of oligogenic/multilocus diseases. Models tailored towards such cases can help shorten the gap of missing diagnoses and can aid researchers in dealing with the high complexity of the derived data. The predictor VarCoPP (Variant Combinations Pathogenicity Predictor) that was published in 2019 and identified potentially pathogenic variant combinations in gene pairs (bilocus variant combinations), was the first important step in this direction. Despite its usefulness and applicability, several issues still remained that hindered a better performance, such as its False Positive (FP) rate, the quality of its training set and its complex architecture. RESULTS: We present VarCoPP2.0: the successor of VarCoPP that is a simplified, faster and more accurate predictive model identifying potentially pathogenic bilocus variant combinations. Results from cross-validation and on independent data sets reveal that VarCoPP2.0 has improved in terms of both sensitivity (95% in cross-validation and 98% during testing) and specificity (5% FP rate). At the same time, its running time shows a significant 150-fold decrease due to the selection of a simpler Balanced Random Forest model. Its positive training set now consists of variant combinations that are more confidently linked with evidence of pathogenicity, based on the confidence scores present in OLIDA, the Oligogenic Diseases Database ( https://olida.ibsquare.be ). The improvement of its performance is also attributed to a more careful selection of up-to-date features identified via an original wrapper method. We show that the combination of different variant and gene pair features together is important for predictions, highlighting the usefulness of integrating biological information at different levels. CONCLUSIONS: Through its improved performance and faster execution time, VarCoPP2.0 enables a more accurate analysis of larger data sets linked to oligogenic diseases. Users can access the ORVAL platform ( https://orval.ibsquare.be ) to apply VarCoPP2.0 on their data.

We consider the optimal performance of blind separation of Gaussian sources. In practice, this estimation problem is solved by a two-step procedure: estimation of a set of covariance matrices from the observed data and approximate joint diagonalization of this set to find the unmixing matrix. Rather than studying the theoretical performance of a specific method, we are interested in the optimal attainable performance of any estimator. To do so, we consider the so-called intrinsic Cramér-Rao bound, which exploits the geometry of the parameters of the model. Unlike previous works developing a Cramér-Rao bound in this context, our solution does not require any additional hypotheses. To obtain our bound, we define and study a new Riemannian manifold holding the parameters of interest. An original estimation error measure is defined with the help of our Riemannian distance function. The corresponding Fisher information matrix is then obtained from the Fisher information metric and orthonormal bases on the tangent spaces of the manifold. Finally, our theoretical results are validated on simulated data.

MOTIVATION: The number of protein records in the UniProt Knowledgebase (UniProtKB: https://www.uniprot.org) continues to grow rapidly as a result of genome sequencing and the prediction of protein-coding genes. Providing functional annotation for these proteins presents a significant and continuing challenge. RESULTS: In response to this challenge, UniProt has developed a method of annotation, known as UniRule, based on expertly curated rules, which integrates related systems (RuleBase, HAMAP, PIRSR, PIRNR) developed by the members of the UniProt consortium. UniRule uses protein family signatures from InterPro, combined with taxonomic and other constraints, to select sets of reviewed proteins which have common functional properties supported by experimental evidence. This annotation is propagated to unreviewed records in UniProtKB that meet the same selection criteria, most of which do not have (and are never likely to have) experimentally verified functional annotation. Release 2020_01 of UniProtKB contains 6496 UniRule rules which provide annotation for 53 million proteins, accounting for 30% of the 178 million records in UniProtKB. UniRule provides scalable enrichment of annotation in UniProtKB. AVAILABILITY AND IMPLEMENTATION: UniRule rules are integrated into UniProtKB and can be viewed at https://www.uniprot.org/unirule/. UniRule rules and the code required to run the rules, are publicly available for researchers who wish to annotate their own sequences. The implementation used to run the rules is known as UniFIRE and is available at https://gitlab.ebi.ac.uk/uniprot-public/unifire.

A growing problem in the remote sensing community concerns the estimation of change-points in a time series of Synthetic Aperture Radar (SAR) images. Although the methodologies of change-point estimation have already been investigated in the literature, there are, to the best of our knowledge, no study on the expected performance for the estimation of change-points in a Wishart distributed time series. This is mainly due to the fact that few results exist on change-point estimation performance in the mathematical literature: the classical central limit theorem does not apply and the classical Cramer-Rao Bound does not exist due to the discrete nature of the parameters. To fill this gap, this paper proposes to use a lower-bound on the Mean Square Error (MSE) with fewer regularity conditions. To this end, recent works on hybrid Cramer-Rao/Weiss-Weinstein bound have been adapted to the specific SAR problematic of interest. Since estimation strategies usually rely on a set of parameters which have to be set by the user, we show how the proposed lower bound allows performing an appropriate tuning. Moreover, the proposed bound is computationally efficient which enables an extensive analysis without a high computational cost.

Scatter matrix and its normalized counterpart, referred to as shape matrix, are key parameters in multivariate statistical signal processing, as they generalize the concept of covariance matrix in the widely used Complex Elliptically Symmetric distributions. Following the framework of [1], intrinsic Cramér-Rao bounds are derived for the problem of scatter and shape matrices estimation with samples following a Complex Elliptically Symmetric distribution. The Fisher Information Metric and its associated Riemannian distance (namely, CES-Fisher) on the manifold of Hermitian positive definite matrices are derived. Based on these results, intrinsic Cramér-Rao bounds on the considered problems are then expressed for three different distances (Euclidean, natural Riemannian, and CES-Fisher). These contributions are therefore a generalization of Theorems 4 and 5 of [1] to a wider class of distributions and metrics for both scatter and shape matrices.

In this letter, we study the behavior of the maximum likelihood estimator (MLE) in the framework of low noise level (or high signal-to-noise ratio), when the data follow a unimodal elliptical distribution. The MLE appears to be the same as in the Gaussian context, regardless the noise distribution. We also show that the asymptotic distribution of this estimator is unimodal elliptical, where the law is intimately linked to that of the noise distribution. Additionally, this estimator is shown to be not efficient, except in the Gaussian noise case. Finally, we validate our analytic results by some simulations.

This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson distribution (continuous parameters) are unknown, it is appropriate to consider a mixed Cramér-Rao/Weiss-Weinstein bound for which we derive closed-form expressions and illustrate its tightness by numerical simulations.

In many deterministic estimation problems, the probability density function (p.d.f.) parameterized by unknown deterministic parameters results from the marginalization of a joint p.d.f. depending on additional random variables. Unfortunately, this marginalization is often mathematically intractable, which prevents from using standard maximum likelihood estimators (MLEs) or any standard lower bound on their mean squared error (MSE). To circumvent this problem, the use of joint MLEs of deterministic and random parameters are proposed as being a substitute. It is shown that, regarding the deterministic parameters: 1) the joint MLEs provide generally suboptimal estimates in any asymptotic regions of operation yielding unbiased efficient estimates, 2) any representative of the two general classes of lower bounds, respectively the Small-Error bounds and the Large-Error bounds, has a “non-standard” version lower bounding the MSE of the deterministic parameters estimate.

A fairly general class of Bayesian “large-error” lower bounds of the Weiss-Weinstein family, essentially free from regularity conditions on the probability density functions support, and for which a limiting form yields a generalized Bayesian Cramér-Rao bound (BCRB), is introduced. In a large number of cases, the generalized BCRB appears to be the Bobrovsky-Mayer-Wolf-Zakai bound (BMZB). Interestingly enough, a regularized form of the Bobrovsky-Zakai bound (BZB), applicable when the support of the prior is a constrained parameter set, is obtained. Modified Weiss-Weinstein bound and BZB which limiting form is the BMZB are proposed, in expectation of an increased tightness in the threshold region. Some of the proposed results are exemplified with a reference problem in signal processing: the Gaussian observation model with parameterized mean and uniform prior.

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. Numerous works have shown the versatility of deterministic constrained Cramér-Rao bound for estimation performance analysis and design of a system of measurement. However in many systems both random and non-random parameters may occur simultaneously. In this communication, we propose a constrained hybrid lower bound which take into account of equality constraint on deterministic parameters. The usefulness of the proposed bound is illustrated with an application to radar Doppler estimation

This letter investigates hybrid lower bounds on the mean square error in order to predict the so-called threshold effect. A new family of tighter hybrid large error bounds based on linear transformations (discrete or integral) of a mixture of the McAulay-Seidman bound and the Weiss-Weinstein bound is provided in multivariate parameters case with multiple test points. For use in applications, we give a closed-form expression of the proposed bound for a set of Gaussian observation models with parameterized mean, including tones estimation which exemplifies the threshold prediction capability of the proposed bound.

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. As a contribution to the hybrid estimation framework, we introduce a recursive hybrid Cramér–Rao lower bound for discrete-time Markovian dynamic systems depending on unknown deterministic parameters. Additionally, the regularity conditions required for its existence and its use are clarified.

In statistical signal processing, hybrid parameter estimation refers to the case where the parameters vector to estimate contains both non-random and random parameters. In this communication, we propose a new hybrid lower bound which, for the first time, includes the Ziv-Zakaï bound well known for its tightness in the Bayesian context (random parameters only). For the general case of parameterized mean model with Gaussian noise, closed-form expressions of the proposed bound are provided.

This article investigates hybrid lower bounds in order to predict the estimators mean square error threshold effect. A tractable and computationally efficient form is derived. This form combines the Barankin and the Weiss-Weinstein bounds. This bound is applied to a frequency estimation problem for which a closed-form expression is provided. A comparison with results on the hybrid Barankin bound shows the superiority of this new bound to predict the mean square error threshold.

In this paper, we derive the Multidimensional Statistical Resolution Limit (MSRL) to resolve two closely spaced targets using a widely spaced MIMO radar. Toward this end, we perform a hypothesis test formulation using the Generalized Likelihood Ratio Test (GLRT). More precisely, we link the MSRL to the minimum Signal-to-Noise Ratio (SNR) required to resolve two closely spaced targets, for a given probability of false alarm and for a given probability of detection. Finally, theoretical and numerical analysis of the MSRL are given for several scenarios (known/unknown parameters of interest and known/unknown noise variance) including lacunar arrays.

In this paper, we study the impact of modeling error on the receiver of a MIMO radar. Following other works on classical array processing, we derive closed-form expressions of the Cramér-Rao bounds for an observation model of a widely spaced MIMO radar affected by modeling error. We show that, as the signal-to-noise ratio increases, the Cramér-Rao bound and the mean square error of the maximum likelihood estimator of the angle-of-arrival do not fall to zero (contrary to the classical case without error modeling) and converge to a fixed limit for which we give a closed-form expression. Moreover, we give a simple closed-form expression of the critical value of the signal-to-noise ratio where this limitation of performance appears.

The concept of Statistical Resolution Limit (SRL), which is defined as the minimal separation to resolve two closely spaced signals, is an important tool to quantify performance in parametric estimation problems. This paper generalizes the SRL based on the Cramér-Rao bound to multiple parameters of interest per signal and for multiple signals. We first provide a fresh look at the SRL in the sense of Smith's criterion by using a proper change of variable formula. Second, based on the Minkowski distances, we extend this criterion to the important case of multiple parameters of interest per signal and to multiple signals. The results presented herein can be applied to any estimation problem and are not limited to source localization problems.

It is well known that in non-linear estimation problems the ML estimator exhibits a threshold effect, i.e. a rapid deterioration of estimation accuracy below a certain SNR or number of snapshots. This effect is caused by outliers and is not captured by standard tools such as the Cramer-Rao bound (CRB). The search of the SNR threshold value can be achieved with the help of approximations of the Barankin bound (BB) proposed by many authors. These approximations result from a linear transformation (discrete or integral) of the uniform unbiasness constraint introduced by Barankin. Nevertheless, non-linear transformations can be used as well for some class of p.d.f. including the Gaussian case. The benefit is their combination with existing linear transformation to get tighter lower bounds improving the SNR threshold prediction.

Near-field source localization problem by a passive antenna array makes the assumption that the time-varying sources are located near the antenna. In this situation, the far-field assumption (planar wavefront) is no longer valid and we have to consider a more complicated model parameterized by the bearing (as in the far-field case) and by the distance, named range, between the source and a reference sensor. We can find a plethora of estimation schemes in the literature but the ultimate performance has not been fully investigated. In this paper, we derive and analyze the Cramer-Rao Bound (CRB) for a single time-varying source. In this case, we obtain nonmatrix closed-form expressions. Our approach has two advantages: (i) the computational cost for a large number of snapshots of a matrix-based CRB can be high while our approach is cheap and (ii) some useful informations can be deduced from the behavior of the bound. In particular, we show that closer is the source from the array and/or higher is the carrier frequency, better is the estimation of the range.

This letter deals with the CramrRao bound for the estimation of a hybrid vector with both random and deterministic parameters. We point out the specificity of the case when the deterministic and the random vectors of parameters are statistically dependent. The relevance of this expression is illustrated by studying a practical phase estimation problem in a non-data-aided communication context.

This letter investigates Bayesian bounds on the mean-square error (MSE) applied to a data-aided carrier estimation problem. The presented bounds are derived from a covariance inequality principle: the so-called Weiss and Weinstein family. These bounds are of utmost interest to find the fundamental MSE limits of an estimator, even for critical scenarios (low signal-to-noise ratio and/or low number of observations). In a data-aided carrier estimation problem, a closed-form expression of the Weiss-Weinstein bound (WWB) that is known to be the tightest bound of the Weiss and Weinstein family is given. A comparison with the maximum likelihood estimator and the other bounds of the Weiss and Weinstein family is given. The WWB is shown to be an efficient tool to approximate this estimator's MSE and to predict the well-known threshold effect

This paper deals with lower bound on the mean square error (MSE). In the Bayesian framework, we present a new bound which is derived from a constrained optimization problem. This bound is found to be tighter than the Bayesian Bhattacharyya bound, the Reuven-Messer bound, the Bobrovsky-Zakai bound, and the Bayesian Cramer-Rao bound

In estimation theory, the asymptotic efficiency of the maximum likelihood (ML) method for independent identically distributed observations and when the number of observations, T, tends to infinity is a well known result. In some scenarios, the number of snapshots may be small, making this result inapplicable. In the array processing framework, for Gaussian emitted signals, we fill this lack at high signal-to-noise ratio (SNR). In this situation, we show that the ML estimation is asymptotically (with respect to SNR) inefficient and non Gaussian.