arXiv subjects

Luca Ambrogioni

Publications and source records attributed to Luca Ambrogioni.

At least 55 records · Page 3Linked to original sources

arXiv2021

Automatic structured variational inference

Stochastic variational inference offers an attractive option as a default method for differentiable probabilistic programming. However, the performance of the variational approach depends on the choice of an appropriate variational family. Here, we introduce automatic structured variational inference (ASVI), a fully automated method for constructing structured variational families, inspired by the closed-form update in conjugate Bayesian models. These convex-update families incorporate the forward pass of the input probabilistic program and can therefore capture complex statistical dependencies. Convex-update families have the same space and time complexity as the input probabilistic program and are therefore tractable for a very large family of models including both continuous and discrete variables. We validate our automatic variational method on a wide range of low- and high-dimensional inference problems. We find that ASVI provides a clear improvement in performance when compared with other popular approaches such as the mean-field approach and inverse autoregressive flows. We provide an open source implementation of ASVI in TensorFlow Probability.

stat.ML↗

arXiv2021

Automatic variational inference with cascading flows

The automation of probabilistic reasoning is one of the primary aims of machine learning. Recently, the confluence of variational inference and deep learning has led to powerful and flexible automatic inference methods that can be trained by stochastic gradient descent. In particular, normalizing flows are highly parameterized deep models that can fit arbitrarily complex posterior densities. However, normalizing flows struggle in highly structured probabilistic programs as they need to relearn the forward-pass of the program. Automatic structured variational inference (ASVI) remedies this problem by constructing variational programs that embed the forward-pass. Here, we combine the flexibility of normalizing flows and the prior-embedding property of ASVI in a new family of variational programs, which we named cascading flows. A cascading flows program interposes a newly designed highway flow architecture in between the conditional distributions of the prior program such as to steer it toward the observed data. These programs can be constructed automatically from an input probabilistic program and can also be amortized automatically. We evaluate the performance of the new variational programs in a series of structured inference problems. We find that cascading flows have much higher performance than both normalizing flows and ASVI in a large set of structured inference problems.

stat.ML↗

arXiv2020

GAIT-prop: A biologically plausible learning rule derived from backpropagation of error

Traditional backpropagation of error, though a highly successful algorithm for learning in artificial neural network models, includes features which are biologically implausible for learning in real neural circuits. An alternative called target propagation proposes to solve this implausibility by using a top-down model of neural activity to convert an error at the output of a neural network into layer-wise and plausible 'targets' for every unit. These targets can then be used to produce weight updates for network training. However, thus far, target propagation has been heuristically proposed without demonstrable equivalence to backpropagation. Here, we derive an exact correspondence between backpropagation and a modified form of target propagation (GAIT-prop) where the target is a small perturbation of the forward pass. Specifically, backpropagation and GAIT-prop give identical updates when synaptic weight matrices are orthogonal. In a series of simple computer vision experiments, we show near-identical performance between backpropagation and GAIT-prop with a soft orthogonality-inducing regularizer.

cs.LG↗

arXiv2020

Explainable 3D Convolutional Neural Networks by Learning Temporal Transformations

In this paper we introduce the temporally factorized 3D convolution (3TConv) as an interpretable alternative to the regular 3D convolution (3DConv). In a 3TConv the 3D convolutional filter is obtained by learning a 2D filter and a set of temporal transformation parameters, resulting in a sparse filter where the 2D slices are sequentially dependent on each other in the temporal dimension. We demonstrate that 3TConv learns temporal transformations that afford a direct interpretation. The temporal parameters can be used in combination with various existing 2D visualization methods. We also show that insight about what the model learns can be achieved by analyzing the transformation parameter statistics on a layer and model level. Finally, we implicitly demonstrate that, in popular ConvNets, the 2DConv can be replaced with a 3TConv and that the weights can be transferred to yield pretrained 3TConvs. pretrained 3TConvnets leverage more than a decade of work on traditional 2DConvNets by being able to make use of features that have been proven to deliver excellent results on image classification benchmarks.

cs.CV↗

arXiv2020

The Indian Chefs Process

This paper introduces the Indian Chefs Process (ICP), a Bayesian nonparametric prior on the joint space of infinite directed acyclic graphs (DAGs) and orders that generalizes Indian Buffet Processes. As our construction shows, the proposed distribution relies on a latent Beta Process controlling both the orders and outgoing connection probabilities of the nodes, and yields a probability distribution on sparse infinite graphs. The main advantage of the ICP over previously proposed Bayesian nonparametric priors for DAG structures is its greater flexibility. To the best of our knowledge, the ICP is the first Bayesian nonparametric model supporting every possible DAG. We demonstrate the usefulness of the ICP on learning the structure of deep generative sigmoid networks as well as convolutional neural networks.

cs.LG↗

arXiv2019

Background Hardly Matters: Understanding Personality Attribution in Deep Residual Networks

Perceived personality traits attributed to an individual do not have to correspond to their actual personality traits and may be determined in part by the context in which one encounters a person. These apparent traits determine, to a large extent, how other people will behave towards them. Deep neural networks are increasingly being used to perform automated personality attribution (e.g., job interviews). It is important that we understand the driving factors behind the predictions, in humans and in deep neural networks. This paper explicitly studies the effect of the image background on apparent personality prediction while addressing two important confounds present in existing literature; overlapping data splits and including facial information in the background. Surprisingly, we found no evidence that background information improves model predictions for apparent personality traits. In fact, when background is explicitly added to the input, a decrease in performance was measured across all models.

cs.LG↗

arXiv2019

Temporal Factorization of 3D Convolutional Kernels

3D convolutional neural networks are difficult to train because they are parameter-expensive and data-hungry. To solve these problems we propose a simple technique for learning 3D convolutional kernels efficiently requiring less training data. We achieve this by factorizing the 3D kernel along the temporal dimension, reducing the number of parameters and making training from data more efficient. Additionally we introduce a novel dataset called Video-MNIST to demonstrate the performance of our method. Our method significantly outperforms the conventional 3D convolution in the low data regime (1 to 5 videos per class). Finally, our model achieves competitive results in the high data regime (>10 videos per class) using up to 45% fewer parameters.

cs.LG↗

arXiv2019

Perturbative estimation of stochastic gradients

In this paper we introduce a family of stochastic gradient estimation techniques based of the perturbative expansion around the mean of the sampling distribution. We characterize the bias and variance of the resulting Taylor-corrected estimators using the Lagrange error formula. Furthermore, we introduce a family of variance reduction techniques that can be applied to other gradient estimators. Finally, we show that these new perturbative methods can be extended to discrete functions using analytic continuation. Using this technique, we derive a new gradient descent method for training stochastic networks with binary weights. In our experiments, we show that the perturbative correction improves the convergence of stochastic variational inference both in the continuous and in the discrete case.

stat.ML↗

arXiv2019

k-GANs: Ensemble of Generative Models with Semi-Discrete Optimal Transport

Generative adversarial networks (GANs) are the state of the art in generative modeling. Unfortunately, most GAN methods are susceptible to mode collapse, meaning that they tend to capture only a subset of the modes of the true distribution. A possible way of dealing with this problem is to use an ensemble of GANs, where (ideally) each network models a single mode. In this paper, we introduce a principled method for training an ensemble of GANs using semi-discrete optimal transport theory. In our approach, each generative network models the transportation map between a point mass (Dirac measure) and the restriction of the data distribution on a tile of a Voronoi tessellation that is defined by the location of the point masses. We iteratively train the generative networks and the point masses until convergence. The resulting k-GANs algorithm has strong theoretical connection with the k-medoids algorithm. In our experiments, we show that our ensemble method consistently outperforms baseline GANs.

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arXiv2019

Wasserstein variational gradient descent: From semi-discrete optimal transport to ensemble variational inference

Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of semi-discrete optimal transport. Instead of minimizing the KL divergence between the posterior and the variational approximation, we minimize a semi-discrete optimal transport divergence. The solution of the resulting optimal transport problem provides both a particle approximation and a set of optimal transportation densities that map each particle to a segment of the posterior distribution. We approximate these transportation densities by minimizing the KL divergence between a truncated distribution and the optimal transport solution. The resulting algorithm can be interpreted as a form of ensemble variational inference where each particle is associated with a local variational approximation.

stat.ML↗

arXiv2018

Wasserstein Variational Inference

This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and the Wasserstein distance as special cases. The gradients of the Wasserstein variational loss are obtained by backpropagating through the Sinkhorn iterations. This technique results in a very stable likelihood-free training method that can be used with implicit distributions and probabilistic programs. Using the Wasserstein variational inference framework, we introduce several new forms of autoencoders and test their robustness and performance against existing variational autoencoding techniques.

stat.ML↗

arXiv2018

Forward Amortized Inference for Likelihood-Free Variational Marginalization

In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a joint-contrastive variational loss. The resulting forward amortized variational inference is a likelihood-free method as its gradient can be sampled without bias and without requiring any evaluation of either the model joint distribution or its derivatives. We prove that our new variational loss is optimized by the exact posterior marginals in the fully factorized mean-field approximation, a property that is not shared with the more conventional reverse KL inference. Furthermore, we show that forward amortized inference can be easily marginalized over large families of latent variables in order to obtain a marginalized variational posterior. We consider two examples of variational marginalization. In our first example we train a Bayesian forecaster for predicting a simplified chaotic model of atmospheric convection. In the second example we train an amortized variational approximation of a Bayesian optimal classifier by marginalizing over the model space. The result is a powerful meta-classification network that can solve arbitrary classification problems without further training.

stat.ML↗

arXiv2017

Complex-valued Gaussian Process Regression for Time Series Analysis

The construction of synthetic complex-valued signals from real-valued observations is an important step in many time series analysis techniques. The most widely used approach is based on the Hilbert transform, which maps the real-valued signal into its quadrature component. In this paper, we define a probabilistic generalization of this approach. We model the observable real-valued signal as the real part of a latent complex-valued Gaussian process. In order to obtain the appropriate statistical relationship between its real and imaginary parts, we define two new classes of complex-valued covariance functions. Through an analysis of simulated chirplets and stochastic oscillations, we show that the resulting Gaussian process complex-valued signal provides a better estimate of the instantaneous amplitude and frequency than the established approaches. Furthermore, the complex-valued Gaussian process regression allows to incorporate prior information about the structure in signal and noise and thereby to tailor the analysis to the features of the signal. As a example, we analyze the non-stationary dynamics of brain oscillations in the alpha band, as measured using magneto-encephalography.

stat.ML↗

arXiv2017

Integral Transforms from Finite Data: An Application of Gaussian Process Regression to Fourier Analysis

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data implicitly assumes periodicity and bandlimitedness of the signal. In this paper, we use Gaussian process regression to estimate the Fourier transform (or any other integral transform) without making these assumptions. This is possible because the posterior expectation of Gaussian process regression maps a finite set of samples to a function defined on the whole real line, expressed as a linear combination of covariance functions. We estimate the covariance function from the data using an appropriately designed gradient ascent method that constrains the solution to a linear combination of tractable kernel functions. This procedure results in a posterior expectation of the analog signal whose Fourier transform can be obtained analytically by exploiting linearity. Our simulations show that the new method leads to sharper and more precise estimation of the spectral density both in noise-free and noise-corrupted signals. We further validate the method in two real-world applications: the analysis of the yearly fluctuation in atmospheric CO2 level and the analysis of the spectral content of brain signals.

stat.ML↗

arXiv2017

The Kernel Mixture Network: A Nonparametric Method for Conditional Density Estimation of Continuous Random Variables

This paper introduces the kernel mixture network, a new method for nonparametric estimation of conditional probability densities using neural networks. We model arbitrarily complex conditional densities as linear combinations of a family of kernel functions centered at a subset of training points. The weights are determined by the outer layer of a deep neural network, trained by minimizing the negative log likelihood. This generalizes the popular quantized softmax approach, which can be seen as a kernel mixture network with square and non-overlapping kernels. We test the performance of our method on two important applications, namely Bayesian filtering and generative modeling. In the Bayesian filtering example, we show that the method can be used to filter complex nonlinear and non-Gaussian signals defined on manifolds. The resulting kernel mixture network filter outperforms both the quantized softmax filter and the extended Kalman filter in terms of model likelihood. Finally, our experiments on generative models show that, given the same architecture, the kernel mixture network leads to higher test set likelihood, less overfitting and more diversified and realistic generated samples than the quantized softmax approach.

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arXiv2017

GP CaKe: Effective brain connectivity with causal kernels

A fundamental goal in network neuroscience is to understand how activity in one region drives activity elsewhere, a process referred to as effective connectivity. Here we propose to model this causal interaction using integro-differential equations and causal kernels that allow for a rich analysis of effective connectivity. The approach combines the tractability and flexibility of autoregressive modeling with the biophysical interpretability of dynamic causal modeling. The causal kernels are learned nonparametrically using Gaussian process regression, yielding an efficient framework for causal inference. We construct a novel class of causal covariance functions that enforce the desired properties of the causal kernels, an approach which we call GP CaKe. By construction, the model and its hyperparameters have biophysical meaning and are therefore easily interpretable. We demonstrate the efficacy of GP CaKe on a number of simulations and give an example of a realistic application on magnetoencephalography (MEG) data.

q-bio.NC↗

arXiv2017

Estimating Nonlinear Dynamics with the ConvNet Smoother

Estimating the state of a dynamical system from a series of noise-corrupted observations is fundamental in many areas of science and engineering. The most well-known method, the Kalman smoother (and the related Kalman filter), relies on assumptions of linearity and Gaussianity that are rarely met in practice. In this paper, we introduced a new dynamical smoothing method that exploits the remarkable capabilities of convolutional neural networks to approximate complex non-linear functions. The main idea is to generate a training set composed of both latent states and observations from an ensemble of simulators and to train the deep network to recover the former from the latter. Importantly, this method only requires the availability of the simulators and can therefore be applied in situations in which either the latent dynamical model or the observation model cannot be easily expressed in closed form. In our simulation studies, we show that the resulting ConvNet smoother has almost optimal performance in the Gaussian case even when the parameters are unknown. Furthermore, the method can be successfully applied to extremely non-linear and non-Gaussian systems. Finally, we empirically validate our approach via the analysis of measured brain signals.

stat.ML↗

arXiv2016

Analysis of Nonstationary Time Series Using Locally Coupled Gaussian Processes

The analysis of nonstationary time series is of great importance in many scientific fields such as physics and neuroscience. In recent years, Gaussian process regression has attracted substantial attention as a robust and powerful method for analyzing time series. In this paper, we introduce a new framework for analyzing nonstationary time series using locally stationary Gaussian process analysis with parameters that are coupled through a hidden Markov model. The main advantage of this framework is that arbitrary complex nonstationary covariance functions can be obtained by combining simpler stationary building blocks whose hidden parameters can be estimated in closed-form. We demonstrate the flexibility of the method by analyzing two examples of synthetic nonstationary signals: oscillations with time varying frequency and time series with two dynamical states. Finally, we report an example application on real magnetoencephalographic measurements of brain activity.

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