arXiv subjects

Patrick Forré

Publications and source records attributed to Patrick Forré.

At least 55 records · Page 3Linked to original sources

arXiv2023

Multi-View Independent Component Analysis with Shared and Individual Sources

Independent component analysis (ICA) is a blind source separation method for linear disentanglement of independent latent sources from observed data. We investigate the special setting of noisy linear ICA where the observations are split among different views, each receiving a mixture of shared and individual sources. We prove that the corresponding linear structure is identifiable, and the source distribution can be recovered. To computationally estimate the sources, we optimize a constrained form of the joint log-likelihood of the observed data among all views. We also show empirically that our objective recovers the sources also in the case when the measurements are corrupted by noise. Furthermore, we propose a model selection procedure for recovering the number of shared sources which we verify empirically. Finally, we apply the proposed model in a challenging real-life application, where the estimated shared sources from two large transcriptome datasets (observed data) provided by two different labs (two different views) lead to recovering (shared) sources utilized for finding a plausible representation of the underlying graph structure.

cs.LG↗

arXiv2023

Combining Interventional and Observational Data Using Causal Reductions

Unobserved confounding is one of the main challenges when estimating causal effects. We propose a causal reduction method that, given a causal model, replaces an arbitrary number of possibly high-dimensional latent confounders with a single latent confounder that takes values in the same space as the treatment variable, without changing the observational and interventional distributions the causal model entails. This allows us to estimate the causal effect in a principled way from combined data without relying on the common but often unrealistic assumption that all confounders have been observed. We apply our causal reduction in three different settings. In the first setting, we assume the treatment and outcome to be discrete. The causal reduction then implies bounds between the observational and interventional distributions that can be exploited for estimation purposes. In certain cases with highly unbalanced observational samples, the accuracy of the causal effect estimate can be improved by incorporating observational data. Second, for continuous variables and assuming a linear-Gaussian model, we derive equality constraints for the parameters of the observational and interventional distributions. Third, for the general continuous setting (possibly nonlinear and non-Gaussian), we parameterize the reduced causal model using normalizing flows, a flexible class of easily invertible nonlinear transformations. We perform a series of experiments on synthetic data and find that in several cases the number of interventional samples can be reduced when adding observational training samples without sacrificing accuracy.

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arXiv2023

Equivariance-aware Architectural Optimization of Neural Networks

Incorporating equivariance to symmetry groups as a constraint during neural network training can improve performance and generalization for tasks exhibiting those symmetries, but such symmetries are often not perfectly nor explicitly present. This motivates algorithmically optimizing the architectural constraints imposed by equivariance. We propose the equivariance relaxation morphism, which preserves functionality while reparameterizing a group equivariant layer to operate with equivariance constraints on a subgroup, as well as the [G]-mixed equivariant layer, which mixes layers constrained to different groups to enable within-layer equivariance optimization. We further present evolutionary and differentiable neural architecture search (NAS) algorithms that utilize these mechanisms respectively for equivariance-aware architectural optimization. Experiments across a variety of datasets show the benefit of dynamically constrained equivariance to find effective architectures with approximate equivariance.

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arXiv2022

Normalizing Flows for Hierarchical Bayesian Analysis: A Gravitational Wave Population Study

We propose parameterizing the population distribution of the gravitational wave population modeling framework (Hierarchical Bayesian Analysis) with a normalizing flow. We first demonstrate the merit of this method on illustrative experiments and then analyze four parameters of the latest LIGO/Virgo data release: primary mass, secondary mass, redshift, and effective spin. Our results show that despite the small and notoriously noisy dataset, the posterior predictive distributions (assuming a prior over the parameters of the flow) of the observed gravitational wave population recover structure that agrees with robust previous phenomenological modeling results while being less susceptible to biases introduced by less flexible models. Therefore, the method forms a promising flexible, reliable replacement for population inference distributions, even when data is highly noisy.

astro-ph.IM↗

arXiv2022

Physics-informed inference of aerial animal movements from weather radar data

Studying animal movements is essential for effective wildlife conservation and conflict mitigation. For aerial movements, operational weather radars have become an indispensable data source in this respect. However, partial measurements, incomplete spatial coverage, and poor understanding of animal behaviours make it difficult to reconstruct complete spatio-temporal movement patterns from available radar data. We tackle this inverse problem by learning a mapping from high-dimensional radar measurements to low-dimensional latent representations using a convolutional encoder. Under the assumption that the latent system dynamics are well approximated by a locally linear Gaussian transition model, we perform efficient posterior estimation using the classical Kalman smoother. A convolutional decoder maps the inferred latent system states back to the physical space in which the known radar observation model can be applied, enabling fully unsupervised training. To encourage physical consistency, we additionally introduce a physics-informed loss term that leverages known mass conservation constraints. Our experiments on synthetic radar data show promising results in terms of reconstruction quality and data-efficiency.

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arXiv2022

Self-Supervised Inference in State-Space Models

We perform approximate inference in state-space models with nonlinear state transitions. Without parameterizing a generative model, we apply Bayesian update formulas using a local linearity approximation parameterized by neural networks. This comes accompanied by a maximum likelihood objective that requires no supervision via uncorrupt observations or ground truth latent states. The optimization backpropagates through a recursion similar to the classical Kalman filter and smoother. Additionally, using an approximate conditional independence, we can perform smoothing without having to parameterize a separate model. In scientific applications, domain knowledge can give a linear approximation of the latent transition maps, which we can easily incorporate into our model. Usage of such domain knowledge is reflected in excellent results (despite our model's simplicity) on the chaotic Lorenz system compared to fully supervised and variational inference methods. Finally, we show competitive results on an audio denoising experiment.

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arXiv2021

Foundations of Structural Causal Models with Cycles and Latent Variables

Structural causal models (SCMs), also known as (nonparametric) structural equation models (SEMs), are widely used for causal modeling purposes. In particular, acyclic SCMs, also known as recursive SEMs, form a well-studied subclass of SCMs that generalize causal Bayesian networks to allow for latent confounders. In this paper, we investigate SCMs in a more general setting, allowing for the presence of both latent confounders and cycles. We show that in the presence of cycles, many of the convenient properties of acyclic SCMs do not hold in general: they do not always have a solution; they do not always induce unique observational, interventional and counterfactual distributions; a marginalization does not always exist, and if it exists the marginal model does not always respect the latent projection; they do not always satisfy a Markov property; and their graphs are not always consistent with their causal semantics. We prove that for SCMs in general each of these properties does hold under certain solvability conditions. Our work generalizes results for SCMs with cycles that were only known for certain special cases so far. We introduce the class of simple SCMs that extends the class of acyclic SCMs to the cyclic setting, while preserving many of the convenient properties of acyclic SCMs. With this paper we aim to provide the foundations for a general theory of statistical causal modeling with SCMs.

stat.ME↗

arXiv2021

An Information-theoretic Approach to Distribution Shifts

Safely deploying machine learning models to the real world is often a challenging process. Models trained with data obtained from a specific geographic location tend to fail when queried with data obtained elsewhere, agents trained in a simulation can struggle to adapt when deployed in the real world or novel environments, and neural networks that are fit to a subset of the population might carry some selection bias into their decision process. In this work, we describe the problem of data shift from a novel information-theoretic perspective by (i) identifying and describing the different sources of error, (ii) comparing some of the most promising objectives explored in the recent domain generalization, and fair classification literature. From our theoretical analysis and empirical evaluation, we conclude that the model selection procedure needs to be guided by careful considerations regarding the observed data, the factors used for correction, and the structure of the data-generating process.

cs.LG↗

arXiv2021

Truncated Marginal Neural Ratio Estimation

Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural simulation-based inference algorithm which simultaneously offers simulation efficiency and fast empirical posterior testability, which is unique among modern algorithms. Our approach is simulation efficient by simultaneously estimating low-dimensional marginal posteriors instead of the joint posterior and by proposing simulations targeted to an observation of interest via a prior suitably truncated by an indicator function. Furthermore, by estimating a locally amortized posterior our algorithm enables efficient empirical tests of the robustness of the inference results. Since scientists cannot access the ground truth, these tests are necessary for trusting inference in real-world applications. We perform experiments on a marginalized version of the simulation-based inference benchmark and two complex and narrow posteriors, highlighting the simulator efficiency of our algorithm as well as the quality of the estimated marginal posteriors.

stat.ML↗

arXiv2021

Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions

Generative flows and diffusion models have been predominantly trained on ordinal data, for example natural images. This paper introduces two extensions of flows and diffusion for categorical data such as language or image segmentation: Argmax Flows and Multinomial Diffusion. Argmax Flows are defined by a composition of a continuous distribution (such as a normalizing flow), and an argmax function. To optimize this model, we learn a probabilistic inverse for the argmax that lifts the categorical data to a continuous space. Multinomial Diffusion gradually adds categorical noise in a diffusion process, for which the generative denoising process is learned. We demonstrate that our method outperforms existing dequantization approaches on text modelling and modelling on image segmentation maps in log-likelihood.

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arXiv2021

Detecting Dispersed Radio Transients in Real Time Using Convolutional Neural Networks

We present a methodology for automated real-time analysis of a radio image data stream with the goal to find transient sources. Contrary to previous works, the transients we are interested in occur on a time-scale where dispersion starts to play a role, so we must search a higher-dimensional data space and yet work fast enough to keep up with the data stream in real time. The approach consists of five main steps: quality control, source detection, association, flux measurement, and physical parameter inference. We present parallelized methods based on convolutions and filters that can be accelerated on a GPU, allowing the pipeline to run in real-time. In the parameter inference step, we apply a convolutional neural network to dynamic spectra that were obtained from the preceding steps. It infers physical parameters, among which the dispersion measure of the transient candidate. Based on critical values of these parameters, an alert can be sent out and data will be saved for further investigation. Experimentally, the pipeline is applied to simulated data and images from AARTFAAC (Amsterdam Astron Radio Transients Facility And Analysis Centre), a transients facility based on the Low-Frequency Array (LOFAR). Results on simulated data show the efficacy of the pipeline, and from real data it discovered dispersed pulses. The current work targets transients on time scales that are longer than the fast transients of beam-formed search, but shorter than slow transients in which dispersion matters less. This fills a methodological gap that is relevant for the upcoming Square-Kilometer Array (SKA). Additionally, since real-time analysis can be performed, only data with promising detections can be saved to disk, providing a solution to the big-data problem that modern astronomy is dealing with.

astro-ph.IM↗

arXiv2021

Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifolds

Motivated by the vast success of deep convolutional networks, there is a great interest in generalizing convolutions to non-Euclidean manifolds. A major complication in comparison to flat spaces is that it is unclear in which alignment a convolution kernel should be applied on a manifold. The underlying reason for this ambiguity is that general manifolds do not come with a canonical choice of reference frames (gauge). Kernels and features therefore have to be expressed relative to arbitrary coordinates. We argue that the particular choice of coordinatization should not affect a network's inference -- it should be coordinate independent. A simultaneous demand for coordinate independence and weight sharing is shown to result in a requirement on the network to be equivariant under local gauge transformations (changes of local reference frames). The ambiguity of reference frames depends thereby on the G-structure of the manifold, such that the necessary level of gauge equivariance is prescribed by the corresponding structure group G. Coordinate independent convolutions are proven to be equivariant w.r.t. those isometries that are symmetries of the G-structure. The resulting theory is formulated in a coordinate free fashion in terms of fiber bundles. To exemplify the design of coordinate independent convolutions, we implement a convolutional network on the Möbius strip. The generality of our differential geometric formulation of convolutional networks is demonstrated by an extensive literature review which explains a large number of Euclidean CNNs, spherical CNNs and CNNs on general surfaces as specific instances of coordinate independent convolutions.

cs.LG↗

arXiv2021

Self Normalizing Flows

Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function class with easy evaluation of the Jacobian determinant, or an efficient estimator thereof. However, these restrictions limit the performance of such density models, frequently requiring significant depth to reach desired performance levels. In this work, we propose Self Normalizing Flows, a flexible framework for training normalizing flows by replacing expensive terms in the gradient by learned approximate inverses at each layer. This reduces the computational complexity of each layer's exact update from $\mathcal{O}(D^3)$ to $\mathcal{O}(D^2)$, allowing for the training of flow architectures which were otherwise computationally infeasible, while also providing efficient sampling. We show experimentally that such models are remarkably stable and optimize to similar data likelihood values as their exact gradient counterparts, while training more quickly and surpassing the performance of functionally constrained counterparts.

cs.LG↗

arXiv2020

Selecting Data Augmentation for Simulating Interventions

Machine learning models trained with purely observational data and the principle of empirical risk minimization \citep{vapnik_principles_1992} can fail to generalize to unseen domains. In this paper, we focus on the case where the problem arises through spurious correlation between the observed domains and the actual task labels. We find that many domain generalization methods do not explicitly take this spurious correlation into account. Instead, especially in more application-oriented research areas like medical imaging or robotics, data augmentation techniques that are based on heuristics are used to learn domain invariant features. To bridge the gap between theory and practice, we develop a causal perspective on the problem of domain generalization. We argue that causal concepts can be used to explain the success of data augmentation by describing how they can weaken the spurious correlation between the observed domains and the task labels. We demonstrate that data augmentation can serve as a tool for simulating interventional data. We use these theoretical insights to derive a simple algorithm that is able to select data augmentation techniques that will lead to better domain generalization.

stat.ML↗

arXiv2020

FlipOut: Uncovering Redundant Weights via Sign Flipping

Modern neural networks, although achieving state-of-the-art results on many tasks, tend to have a large number of parameters, which increases training time and resource usage. This problem can be alleviated by pruning. Existing methods, however, often require extensive parameter tuning or multiple cycles of pruning and retraining to convergence in order to obtain a favorable accuracy-sparsity trade-off. To address these issues, we propose a novel pruning method which uses the oscillations around $0$ (i.e. sign flips) that a weight has undergone during training in order to determine its saliency. Our method can perform pruning before the network has converged, requires little tuning effort due to having good default values for its hyperparameters, and can directly target the level of sparsity desired by the user. Our experiments, performed on a variety of object classification architectures, show that it is competitive with existing methods and achieves state-of-the-art performance for levels of sparsity of $99.6\%$ and above for most of the architectures tested. For reproducibility, we release our code publicly at https://github.com/AndreiXYZ/flipout.

cs.LG↗

arXiv2020

Improving Fair Predictions Using Variational Inference In Causal Models

The importance of algorithmic fairness grows with the increasing impact machine learning has on people's lives. Recent work on fairness metrics shows the need for causal reasoning in fairness constraints. In this work, a practical method named FairTrade is proposed for creating flexible prediction models which integrate fairness constraints on sensitive causal paths. The method uses recent advances in variational inference in order to account for unobserved confounders. Further, a method outline is proposed which uses the causal mechanism estimates to audit black box models. Experiments are conducted on simulated data and on a real dataset in the context of detecting unlawful social welfare. This research aims to contribute to machine learning techniques which honour our ethical and legal boundaries.

cs.LG↗

arXiv2020

Pruning via Iterative Ranking of Sensitivity Statistics

With the introduction of SNIP [arXiv:1810.02340v2], it has been demonstrated that modern neural networks can effectively be pruned before training. Yet, its sensitivity criterion has since been criticized for not propagating training signal properly or even disconnecting layers. As a remedy, GraSP [arXiv:2002.07376v1] was introduced, compromising on simplicity. However, in this work we show that by applying the sensitivity criterion iteratively in smaller steps - still before training - we can improve its performance without difficult implementation. As such, we introduce 'SNIP-it'. We then demonstrate how it can be applied for both structured and unstructured pruning, before and/or during training, therewith achieving state-of-the-art sparsity-performance trade-offs. That is, while already providing the computational benefits of pruning in the training process from the start. Furthermore, we evaluate our methods on robustness to overfitting, disconnection and adversarial attacks as well.

cs.LG↗

arXiv2020

Neural Ordinary Differential Equations on Manifolds

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately current approaches fall short when the underlying space has a non trivial topology, and are only available for the most basic geometries. Recently normalizing flows in Euclidean space based on Neural ODEs show great promise, yet suffer the same limitations. Using ideas from differential geometry and geometric control theory, we describe how neural ODEs can be extended to smooth manifolds. We show how vector fields provide a general framework for parameterizing a flexible class of invertible mapping on these spaces and we illustrate how gradient based learning can be performed. As a result we define a general methodology for building normalizing flows on manifolds.

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