In this work, we consider the identifiability assumption of Gaussian structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that linear Gaussian structural equation models are fully identifiable if all error variances are the same or known. Hence, this work proves the identifiability of Gaussian SEMs with both homogeneous and heterogeneous unknown error variances. Our new identifiability assumption exploits not only error variances, but edge weights; hence, it is strictly milder than prior work on the identifiability result. We further provide a structure learning algorithm that is statistically consistent and computationally feasible, based on our new assumption. The proposed algorithm assumes that all relevant variables are observed, while it does not assume causal minimality and faithfulness. We verify our theoretical findings through simulations, and compare our algorithm to state-of-the-art PC, GES and GDS algorithms.

Crowdsourcing has become widely used in supervised scenarios where training sets are scarce and difficult to obtain. Most crowdsourcing models in the literature assume labelers can provide answers to full questions. In classification contexts, full questions require a labeler to discern among all possible classes. Unfortunately, discernment is not always easy in realistic scenarios. Labelers may not be experts in differentiating all classes. In this work, we provide a full probabilistic model for a shorter type of queries. Our shorter queries only require "yes" or "no" responses. Our model estimates a joint posterior distribution of matrices related to labelers' confusions and the posterior probability of the class of every object. We developed an approximate inference approach, using Monte Carlo Sampling and Black Box Variational Inference, which provides the derivation of the necessary gradients. We built two realistic crowdsourcing scenarios to test our model. The first scenario queries for irregular astronomical time-series. The second scenario relies on the image classification of animals. We achieved results that are comparable with those of full query crowdsourcing. Furthermore, we show that modeling labelers' failures plays an important role in estimating true classes. Finally, we provide the community with two real datasets obtained from our crowdsourcing experiments. All our code is publicly available.

The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational characterizations that naturally suggest a two-step scheme for their optimization, based on the iterative shift of a probability density and the calculation of a best Gaussian approximation in Kullback-Leibler divergence. Under this unified light, the optimization schemes for local entropy and heat regularized loss differ only over which argument of the Kullback-Leibler divergence is used to find the best Gaussian approximation. Local entropy corresponds to minimizing over the second argument, and the solution is given by moment matching. This allows to replace traditional back-propagation calculation of gradients by sampling algorithms, opening an avenue for gradient-free, parallelizable training of neural networks.

We propose a general test of conditional independence. The conditional predictive impact (CPI) is a provably consistent and unbiased estimator of one or several features' association with a given outcome, conditional on a (potentially empty) reduced feature set. The measure can be calculated using any supervised learning algorithm and loss function. It relies on no parametric assumptions and applies equally well to continuous and categorical predictors and outcomes. The CPI can be efficiently computed for low- or high-dimensional data without any sparsity constraints. We illustrate PAC-Bayesian convergence rates for the CPI and develop statistical inference procedures for evaluating its magnitude, significance, and precision. These tests aid in feature and model selection, extending traditional frequentist and Bayesian techniques to general supervised learning tasks. The CPI may also be used in conjunction with causal discovery algorithms to identify underlying graph structures for multivariate systems. We test our method in conjunction with various algorithms, including linear regression, neural networks, random forests, and support vector machines. Empirical results show that the CPI compares favorably to alternative variable importance measures and other nonparametric tests of conditional independence on a diverse array of real and simulated datasets. Simulations confirm that our inference procedures successfully control Type I error and achieve nominal coverage probability. Our method has been implemented in an R package, cpi, which can be downloaded from https://github.com/dswatson/cpi.

We consider the problem of differential privacy accounting, i.e. estimation of privacy loss bounds, in machine learning in a broad sense. We propose two versions of a generic privacy accountant suitable for a wide range of learning algorithms. Both versions are derived in a simple and principled way using well-known tools from probability theory, such as concentration inequalities. We demonstrate that our privacy accountant is able to achieve state-of-the-art estimates of DP guarantees and can be applied to new areas like variational inference. Moreover, we show that the latter enjoys differential privacy at minor cost.

While harms of allocation have been increasingly studied as part of the subfield of algorithmic fairness, harms of representation have received considerably less attention. In this paper, we formalize two notions of stereotyping and show how they manifest in later allocative harms within the machine learning pipeline. We also propose mitigation strategies and demonstrate their effectiveness on synthetic datasets.

The notion of flat minima has played a key role in the generalization studies of deep learning models. However, existing definitions of the flatness are known to be sensitive to the rescaling of parameters. The issue suggests that the previous definitions of the flatness might not be a good measure of generalization, because generalization is invariant to such rescalings. In this paper, from the PAC-Bayesian perspective, we scrutinize the discussion concerning the flat minima and introduce the notion of normalized flat minima, which is free from the known scale dependence issues. Additionally, we highlight the scale dependence of existing matrix-norm based generalization error bounds similar to the existing flat minima definitions. Our modified notion of the flatness does not suffer from the insufficiency, either, suggesting it might provide better hierarchy in the hypothesis class.

Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite difficult, the use of a single kernel type may not be appropriate in all areas of the input space, convergence problems for some kernels are not uncommon, the standard quadratic programming solution has $O(m^3)$ time and $O(m^2)$ space complexity for $m$ training patterns. Kernel methods work because they implicitly provide new, useful features. Such features, derived from various kernels and other vector transformations, may be used directly in any machine learning algorithm, facilitating multiresolution, heterogeneous models of data. Therefore Support Feature Machines (SFM) based on linear models in the extended feature spaces, enabling control over selection of support features, give at least as good results as any kernel-based SVMs, removing all problems related to interpretation, scaling and convergence. This is demonstrated for a number of benchmark datasets analyzed with linear discrimination, SVM, decision trees and nearest neighbor methods.

The Maximum Mutual Information (MMI) criterion is different from the Least Error Rate (LER) criterion. It can reduce failing to report small probability events. This paper introduces the Channels Matching (CM) algorithm for the MMI classifications of unseen instances. It also introduces some semantic information methods, which base the CM algorithm. In the CM algorithm, label learning is to let the semantic channel match the Shannon channel (Matching I) whereas classifying is to let the Shannon channel match the semantic channel (Matching II). We can achieve the MMI classifications by repeating Matching I and II. For low-dimensional feature spaces, we only use parameters to construct n likelihood functions for n different classes (rather than to construct partitioning boundaries as gradient descent) and expresses the boundaries by numerical values. Without searching in parameter spaces, the computation of the CM algorithm for low-dimensional feature spaces is very simple and fast. Using a two-dimensional example, we test the speed and reliability of the CM algorithm by different initial partitions. For most initial partitions, two iterations can make the mutual information surpass 99% of the convergent MMI. The analysis indicates that for high-dimensional feature spaces, we may combine the CM algorithm with neural networks to improve the MMI classifications for faster and more reliable convergence.

In this paper we propose a Bayesian method for estimating architectural parameters of neural networks, namely layer size and network depth. We do this by learning concrete distributions over these parameters. Our results show that regular networks with a learnt structure can generalise better on small datasets, while fully stochastic networks can be more robust to parameter initialisation. The proposed method relies on standard neural variational learning and, unlike randomised architecture search, does not require a retraining of the model, thus keeping the computational overhead at minimum.