Inference for population genetics models is hindered by computationally intractable likelihoods. While this issue is tackled by likelihood-free methods, these approaches typically rely on hand-crafted summary statistics of the data. In complex settings, designing and selecting suitable summary statistics is problematic and results are very sensitive to such choices. In this paper, we learn the first exchangeable feature representation for population genetic data to work directly with genotype data. This is achieved by means of a novel Bayesian likelihood-free inference framework, where a permutation-invariant convolutional neural network learns the inverse functional relationship from the data to the posterior. We leverage access to scientific simulators to learn such likelihood-free function mappings, and establish a general framework for inference in a variety of simulation-based tasks. We demonstrate the power of our method on the recombination hotspot testing problem, outperforming the state-of-the-art.
The inferential accuracy and scalability of these methods can be improved by exploiting symmetries in the input data. Permutation-invariant models have been previously studied in machine learning for SVMs @cite_30 and, recently, gained a surge of interest in the deep learning literature. Recent work on designing architectures for exchangeable data include , , and , which exploit parameter sharing to encode invariances. To our knowledge, no prior work has been done on learning feature representations for exchangeable population genetic data.
@cite_30
2182587296 2147860648 2897830718 2096633407
We study the problem of classifying actions of human subjects using depth movies generated by Kinect or other depth sensors. Representing human body as dynamical skeletons, we study the evolution of their (skeletons’) shapes as trajectories on Kendall’s shape manifold. The action data is typically corrupted by large variability in execution rates within and across subjects and, thus, causing major problems in statistical analyses. To address that issue, we adopt a recently-developed framework of [1] , [2] to this problem domain. Here, the variable execution rates correspond to re-parameterizations of trajectories, and one uses a parameterization-invariant metric for aligning, comparing, averaging, and modeling trajectories. This is based on a combination of transported square-root vector fields (TSRVFs) of trajectories and the standard Euclidean norm, that allows computational efficiency. We develop a comprehensive suite of computational tools for this application domain: smoothing and denoising skeleton trajectories using median filtering, up- and down-sampling actions in time domain, simultaneous temporal-registration of multiple actions, and extracting invertible Euclidean representations of actions. Due to invertibility these Euclidean representations allow both discriminative and generative models for statistical analysis. For instance, they can be used in a SVM-based classification of original actions, as demonstrated here using MSR Action-3D, MSR Daily Activity and 3D Action Pairs datasets. Using only the skelet al information, we achieve state-of-the-art classification results on these datasets. Convolutional neural networks (CNNs) have been successfully applied to many tasks such as digit and object recognition. Using convolutional (tied) weights significantly reduces the number of parameters that have to be learned, and also allows translational invariance to be hard-coded into the architecture. In this paper, we consider the problem of learning invariances, rather than relying on hard-coding. We propose tiled convolution neural networks (Tiled CNNs), which use a regular "tiled" pattern of tied weights that does not require that adjacent hidden units share identical weights, but instead requires only that hidden units k steps away from each other to have tied weights. By pooling over neighboring units, this architecture is able to learn complex invariances (such as scale and rotational invariance) beyond translational invariance. Further, it also enjoys much of CNNs' advantage of having a relatively small number of learned parameters (such as ease of learning and greater scalability). We provide an efficient learning algorithm for Tiled CNNs based on Topographic ICA, and show that learning complex invariant features allows us to achieve highly competitive results for both the NORB and CIFAR-10 datasets. With the growing adoption of machine learning, sharing of learned models is becoming popular. However, in addition to the prediction properties the model producer aims to share, there is also a risk that the model consumer can infer other properties of the training data the model producer did not intend to share. In this paper, we focus on the inference of global properties of the training data, such as the environment in which the data was produced, or the fraction of the data that comes from a certain class, as applied to white-box Fully Connected Neural Networks (FCNNs). Because of their complexity and inscrutability, FCNNs have a particularly high risk of leaking unexpected information about their training sets; at the same time, this complexity makes extracting this information challenging. We develop techniques that reduce this complexity by noting that FCNNs are invariant under permutation of nodes in each layer. We develop our techniques using representations that capture this invariance and simplify the information extraction task. We evaluate our techniques on several synthetic and standard benchmark datasets and show that they are very effective at inferring various data properties. We also perform two case studies to demonstrate the impact of our attack. In the first case study we show that a classifier that recognizes smiling faces also leaks information about the relative attractiveness of the individuals in its training set. In the second case study we show that a classifier that recognizes Bitcoin mining from performance counters also leaks information about whether the classifier was trained on logs from machines that were patched for the Meltdown and Spectre attacks. The ubiquitous need for analyzing privacy-sensitive information—including health records, personal communications, product ratings and social network data—is driving significant interest in privacy-preserving data analysis across several research communities. This paper explores the release of Support Vector Machine (SVM) classifiers while preserving the privacy of training data. The SVM is a popular machine learning method that maps data to a high-dimensional feature space before learning a linear decision boundary. We present efficient mechanisms for finite-dimensional feature mappings and for (potentially infinite-dimensional) mappings with translation-invariant kernels. In the latter case, our mechanism borrows a technique from large-scale learning to learn in a finite-dimensional feature space whose inner-product uniformly approximates the desired feature space inner-product (the desired kernel) with high probability. Differential privacy is established using algorithmic stability, a property used in learning theory to bound generalization error. Utility—when the private classifier is pointwise close to the non-private classifier with high probability—is proven using smoothness of regularized empirical risk minimization with respect to small perturbations to the feature mapping. Finally we conclude with lower bounds on the differential privacy of any mechanism approximating the SVM.