In this paper, we propose an approach for Facial Expressions Recognition (FER) based on a deep multi-facial patches aggregation network. Deep features are learned from facial patches using deep sub-networks and aggregated within one deep architecture for expression classification . Several problems may affect the performance of deep-learning based FER approaches, in particular, the small size of existing FER datasets which might not be sufficient to train large deep learning networks. Moreover, it is extremely time-consuming to collect and annotate a large number of facial images. To account for this, we propose two data augmentation techniques for facial expression generation to expand FER labeled training datasets. We evaluate the proposed framework on three FER datasets. Results show that the proposed approach achieves state-of-art FER deep learning approaches performance when the model is trained and tested on images from the same dataset. Moreover, the proposed data augmentation techniques improve the expression recognition rate, and thus can be a solution for training deep learning FER models using small datasets. The accuracy degrades significantly when testing for dataset bias.

We introduce Deep Sigma Point Processes, a class of parametric models inspired by the compositional structure of Deep Gaussian Processes (DGPs). Deep Sigma Point Processes (DSPPs) retain many of the attractive features of (variational) DGPs, including mini-batch training and predictive uncertainty that is controlled by kernel basis functions. Importantly, since DSPPs admit a simple maximum likelihood inference procedure, the resulting predictive distributions are not degraded by any posterior approximations. In an extensive empirical comparison on univariate and multivariate regression tasks we find that the resulting predictive distributions are significantly better calibrated than those obtained with other probabilistic methods for scalable regression, including variational DGPs--often by as much as a nat per datapoint.

Bayesian reward learning from demonstrations enables rigorous safety and uncertainty analysis when performing imitation learning. However, Bayesian reward learning methods are typically computationally intractable for complex control problems. We propose a highly efficient Bayesian reward learning algorithm that scales to high-dimensional imitation learning problems by first pre-training a low-dimensional feature encoding via self-supervised tasks and then leveraging preferences over demonstrations to perform fast Bayesian inference. We evaluate our proposed approach on the task of learning to play Atari games from demonstrations, without access to the game score. For Atari games our approach enables us to generate 100,000 samples from the posterior over reward functions in only 5 minutes using a personal laptop. Furthermore, our proposed approach achieves comparable or better imitation learning performance than state-of-the-art methods that only find a point estimate of the reward function. Finally, we show that our approach enables efficient high-confidence policy performance bounds. We show that these high-confidence performance bounds can be used to rank the performance and risk of a variety of evaluation policies, despite not having samples of the reward function. We also show evidence that high-confidence performance bounds can be used to detect reward hacking in complex imitation learning problems.

Recent advances in machine learning highlight successes on a small set of tasks where a large number of labeled examples have been collected and exploited. These include image classification with 1.2 million labeled examples Deng et al. (2009) and French-English machine translation with 40 million paired sentences Bojar et al. (2014). For common tasks, however, collecting clean labels is costly, as they require human expertise (as in medical imaging) or physical interactions (as in robotics), for example. Thus collected real-world datasets follow a long-tailed distribution, in which a dominant set of tasks only have a small number of training examples Wang et al. (2017). Inspired by human ingenuity in quickly solving novel problems by leveraging prior experience, meta-learning approaches aim to jointly learn from past experience to quickly adapt to new tasks with little available data Schmidhuber (1987); Thrun & Pratt (2012). This has had a significant impact in few-shot supervised learning, where each task is associated with only a few training examples. By leveraging structural similarities among those tasks, one can achieve accuracy far greater than what can be achieved for each task in isolation Finn et al. (2017); Ravi & Larochelle (2016); Koch et al. (2015); Oreshkin et al. (2018); Triantafillou et al. (2019); Rusu et al. (2018). The success of such approaches hinges on the following fundamental question: When can we jointly train small data tasks to achieve the accuracy of large data tasks? We investigate this tradeoff under a canonical scenario where the tasks are linear regressions in d-dimensions and the regression parameters are drawn i.i.d.

Statistical inference using pairwise comparison data has been an effective approach to analyzing complex and sparse networks. In this paper we propose a general framework for modeling the mutual interaction in a probabilistic network, which enjoys ample flexibility in terms of parametrization. Within this set-up, we establish that the maximum likelihood estimator (MLE) for the latent scores of the subjects is uniformly consistent under a near-minimal condition on network sparsity. This condition is sharp in terms of the leading order asymptotics describing the sparsity. The proof utilizes a novel chaining technique based on the error-induced metric as well as careful counting of comparison graph structures. Our results guarantee that the MLE is a valid estimator for inference in large-scale comparison networks where data is asymptotically deficient. Numerical simulations are provided to complement the theoretical analysis.

The key distinguishing property of a Bayesian approach is marginalization, rather than using a single setting of weights. Bayesian marginalization can particularly improve the accuracy and calibration of modern deep neural networks, which are typically underspecified by the data, and can represent many compelling but different solutions. We show that deep ensembles provide an effective mechanism for approximate Bayesian marginalization, and propose a related approach that further improves the predictive distribution by marginalizing within basins of attraction, without significant overhead. We also investigate the prior over functions implied by a vague distribution over neural network weights, explaining the generalization properties of such models from a probabilistic perspective. From this perspective, we explain results that have been presented as mysterious and distinct to neural network generalization, such as the ability to fit images with random labels, and show that these results can be reproduced with Gaussian processes. Finally, we provide a Bayesian perspective on tempering for calibrating predictive distributions.

Classifying our data and predicting the outcomes from our historical data are huge tasks at the moment. For performing these tasks, we have a robust family of Supervised Learning Algorithms called Naive Bayes' Classifiers. Naive Bayes' Classifiers are wholly based on the Bayes' Theorem which gives us the probability of an event, given that another event has already occurred. This is symbolically expressed as P(A B), i.e. Probability of event A will occur given that event B has already occurred.

We introduce Information Condensing Active Learning (ICAL), a batch mode model agnostic Active Learning (AL) method targeted at Deep Bayesian Active Learning that focuses on acquiring labels for points which have as much information as possible about the still unacquired points. ICAL uses the Hilbert Schmidt Independence Criterion (HSIC) to measure the strength of the dependency between a candidate batch of points and the unlabeled set. We develop key optimizations that allow us to scale our method to large unlabeled sets. We show significant improvements in terms of model accuracy and negative log likelihood (NLL) on several image datasets compared to state of the art batch mode AL methods for deep learning.

Separating high-dimensional data like images into independent latent factors remains an open research problem. Here we develop a method that jointly learns a linear independent component analysis (ICA) model with non-linear bijective feature maps. By combining these two methods, ICA can learn interpretable latent structure for images. For non-square ICA, where we assume the number of sources is less than the dimensionality of data, we achieve better unsupervised latent factor discovery than flow-based models and linear ICA. This performance scales to large image datasets such as CelebA.

We address the problem of the achievable regret rates with online logistic regression. We derive lower bounds with logarithmic regret under $L_1$, $L_2$, and $L_\infty$ constraints on the parameter values. The bounds are dominated by $d/2 \log T$, where $T$ is the horizon and $d$ is the dimensionality of the parameter space. We show their achievability for $d=o(T^{1/3})$ in all these cases with Bayesian methods, that achieve them up to a $d/2 \log d$ term. Interesting different behaviors are shown for larger dimensionality. Specifically, on the negative side, if $d = \Omega(\sqrt{T})$, any algorithm is guaranteed regret of $\Omega(d \log T)$ (greater than $\Omega(\sqrt{T})$) under $L_\infty$ constraints on the parameters (and the example features). On the positive side, under $L_1$ constraints on the parameters, there exist algorithms that can achieve regret that is sub-linear in $d$ for the asymptotically larger values of $d$. For $L_2$ constraints, it is shown that for large enough $d$, the regret remains linear in $d$ but no longer logarithmic in $T$. Adapting the redundancy-capacity theorem from information theory, we demonstrate a principled methodology based on grids of parameters to derive lower bounds. Grids are also utilized to derive some upper bounds. Our results strengthen results by Kakade and Ng (2005) and Foster et al. (2018) for upper bounds for this problem, introduce novel lower bounds, and adapt a methodology that can be used to obtain such bounds for other related problems. They also give a novel characterization of the asymptotic behavior when the dimension of the parameter space is allowed to grow with $T$. They additionally establish connections to the information theory literature, demonstrating that the actual regret for logistic regression depends on the richness of the parameter class, where even within this problem, richer classes lead to greater regret.