In this article, we propose a new variational approach to learn private and/or fair representations. This approach is based on the Lagrangians of a new formulation of the privacy and fairness optimization problems that we propose. In this formulation, we aim at generating representations of the data that keep a prescribed level of the relevant information that is not shared by the private or sensitive data, while minimizing the remaining information they keep. The proposed approach (i) exhibits the similarities of the privacy and fairness problems, (ii) allows us to control the trade-off between utility and privacy or fairness through the Lagrange multiplier parameter, and (iii) can be comfortably incorporated to common representation learning algorithms such as the VAE, the $\beta$-VAE, the VIB, or the nonlinear IB.

Stochastic optimization is the process of minimizing a deterministic objective function via the simulation of random elements, and it is one of the most successful methods for optimizing complex or unknown objectives. Relatively simple stochastic optimization procedures--in particular, stochastic gradient descent (SGD)--have become the backbone of modern machine learning (ML) [50]. To improve understanding of stochastic optimization in ML, and particularly why SGD and its extensions work so well, recent theoretical work has sought to study its properties and dynamics [47]. Such analyses typically approach the problem through one of two perspectives. The first perspective, an optimization (or quenching) perspective, examines convergence either in expectation [11, 20, 28, 60, 84] or with some positive (high) probability [19, 41, 66, 77] through the lens of a deterministic counterpart. This perspective inherits some limitations of deterministic optimizers, including assumptions (e.g., convexity, Polyak-Łojasiewicz criterion, etc.) that are either not satisfied by state-of-the-art problems, or not strong enough to imply convergence to a quality (e.g., global) optimum. More concerning, however, is the inability to explain what has come to be known as the "generalization gap" phenomenon: increasing stochasticity by reducing batch size appears to improve generalization performance [38, 55]. Empirically, existing strategies do tend to break down for inference tasks when using large batch sizes [27].

In real-world classification problems, pairwise supervision (i.e., a pair of patterns with a binary label indicating whether they belong to the same class or not) can often be obtained at a lower cost than ordinary class labels. Similarity learning is a general framework to utilize such pairwise supervision to elicit useful representations by inferring the relationship between two data points, which encompasses various important preprocessing tasks such as metric learning, kernel learning, graph embedding, and contrastive representation learning. Although elicited representations are expected to perform well in downstream tasks such as classification, little theoretical insight has been given in the literature so far. In this paper, we reveal that a specific formulation of similarity learning is strongly related to the objective of binary classification, which spurs us to learn a binary classifier without ordinary class labels---by fitting the product of real-valued prediction functions of pairwise patterns to their similarity. Our formulation of similarity learning does not only generalize many existing ones, but also admits an excess risk bound showing an explicit connection to classification. Finally, we empirically demonstrate the practical usefulness of the proposed method on benchmark datasets.

In over two decades of research, the field of dictionary learning has gathered a large collection of successful applications, and theoretical guarantees for model recovery are known only whenever optimization is carried out in the same model class as that of the underlying dictionary. This work characterizes the surprising phenomenon that dictionary recovery can be facilitated by searching over the space of larger over-realized models. This observation is general and independent of the specific dictionary learning algorithm used. We thoroughly demonstrate this observation in practice and provide a theoretical analysis of this phenomenon by tying recovery measures to generalization bounds. We further show that an efficient and provably correct distillation mechanism can be employed to recover the correct atoms from the over-realized model. As a result, our meta-algorithm provides dictionary estimates with consistently better recovery of the ground-truth model.

Dynamic Distribution Decomposition (DDD) was introduced in Taylor-King et al. [30] as a variation on Dynamic Mode Decomposition. In brief, by using basis functions over a continuous state space, DDD allows for the fitting of continuoustime Markov chains over these basis functions and as a result continuously maps between distributions. The number of parameters in DDD scales by the square of the number of basis functions; we reformulate the problem and restrict the method to compact basis functions which leads to the inference of sparse matrices only -- hence reducing the number of parameters. Finally, we demonstrate how DDD is suitable to integrate both trajectory time series (paired between subsequent time points) and snapshot time series (unpaired time points). Methods capable of integrating both scenarios are particularly relevant for the analysis of biomedical data, whereby studies observe population at fixed time points (snapshots) and individual patient journeys with repeated follow ups (trajectories).

The robustness of classifiers has become a question of paramount importance in the past few years. Indeed, it has been shown that state-of-the-art deep learning architectures can easily be fooled with imperceptible changes to their inputs. Therefore, finding good measures of robustness of a trained classifier is a key issue in the field. In this paper, we point out that averaging the radius of robustness of samples in a validation set is a statistically weak measure. We propose instead to weight the importance of samples depending on their difficulty. We motivate the proposed score by a theoretical case study using logistic regression, where we show that the proposed score is independent of the choice of the samples it is evaluated upon. We also empirically demonstrate the ability of the proposed score to measure robustness of classifiers with little dependence on the choice of samples in more complex settings, including deep convolutional neural networks and real datasets.

Causal modeling has been recognized as a potential solution to many challenging problems in machine learning (ML). Here, we propose a counterfactual approach to remove/reduce the influence of confounders from the predictions generated a deep neural network (DNN). Rather than attempting to prevent DNNs from directly learning the confounding signal, we propose a counterfactual approach to remove confounding from the feature representations learned by DNNs in anticausal prediction tasks. By training an accurate DNN using softmax activation at the classification layer, and then adopting the representation learned by the last layer prior to the output layer as our features, we have that, by construction, the learned features will fit well a logistic regression model, and will be linearly associated with the labels. Then, in order to generate classifiers that are free from the influence of the observed confounders we: (i) use linear models to regress each learned feature on the labels and on the confounders and estimate the respective regression coefficients and model residuals; (ii) generate new counterfactual features by adding back to the estimated residuals to a linear predictor which no longer includes the confounder variables; and (iii) train and evaluate a logistic classifier using the counterfactual features as inputs. We validate the proposed methodology using colored versions of the MNIST and fashion-MNIST datasets, and show how the approach can effectively combat confounding and improve generalization in the context of dataset shift. Comparison against a variation of the SMOTE \cite{chawla2002} approach showed that the causality-aware approach compared favorably against SMOTE balancing in our experiments. Finally, we also describe how to use conditional independence tests to evaluate if the counterfactual approach has effectively removed the confounder signals from the predictions.

Generative Adversarial Network (GAN) can be viewed as an implicit estimator of a data distribution, and this perspective motivates using the adversarial concept in the true input parameter estimation of black-box generators. While previous works on likelihood-free inference introduces an implicit proposal distribution on the generator input, this paper analyzes theoretic limitations of the proposal distribution approach. On top of that, we introduce a new algorithm, Adversarial Likelihood-Free Inference (ALFI), to mitigate the analyzed limitations, so ALFI is able to find the posterior distribution on the input parameter for black-box generative models. We experimented ALFI with diverse simulation models as well as pre-trained statistical models, and we identified that ALFI achieves the best parameter estimation accuracy with a limited simulation budget.

With a myriad of resources out there explaining gradient descents, in this post, I'd like to visually walk you through how each of these methods works. With the aid of a gradient descent visualization tool I built, hopefully I can present you with some unique insights, or minimally, many GIFs. I assume basic familiarity of why and how gradient descent is used in machine learning (if not, I recommend this video by 3Blue1Brown) . My focus here is to compare and contrast these methods. If you are already familiar with all the methods, you can scroll to the bottom to watch a few fun "horse races".

We create a computationally tractable algorithm for contextual bandits with continuous actions having unknown structure. Our reduction-style algorithm composes with most supervised learning representations. We prove that it works in a general sense and verify the new functionality with large-scale experiments.