We use CNNs to build a system that both classifies images of faces based on a variety of different facial attributes and generates new faces given a set of desired facial characteristics. After introducing the problem and providing context in the first section, we discuss recent work related to image generation in Section 2. In Section 3, we describe the methods used to fine-tune our CNN and generate new images using a novel approach inspired by a Gaussian mixture model. In Section 4, we discuss our working dataset and describe our preprocessing steps and handling of facial attributes. Finally, in Sections 5, 6 and 7, we explain our experiments and results and conclude in the following section. Our classification system has 82 test accuracy. Furthermore, our generation pipeline successfully creates well-formed faces.
Finally, another approach for estimating generative models is via generative adversarial nets @cite_9 @cite_5 . In this framework, two models are simultaneously trained: a generative model @math that captures the distribution of the data and a discriminative model @math that estimates the probability that a sample came from the training data rather than @math . @math is trained to maximize the probability that @math makes a mistake.
@cite_5 @cite_9
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We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples. Deep learning-based robotic grasping has made significant progress the past several years thanks to algorithmic improvements and increased data availability. However, state-of-the-art models are often trained on as few as hundreds or thousands of unique object instances, and as a result generalization can be a challenge. In this work, we explore a novel data generation pipeline for training a deep neural network to perform grasp planning that applies the idea of to object synthesis. We generate millions of unique, unrealistic procedurally generated objects, and train a deep neural network to perform grasp planning on these objects. Since the distribution of successful grasps for a given object can be highly multimodal, we propose an autoregressive grasp planning model that maps sensor inputs of a scene to a probability distribution @math , where @math corresponds to the model's estimate of the normalized probability of success of the grasp @math conditioned on the observations @math . Our model allows us to sample grasps efficiently at test time (or avoid sampling entirely). We evaluate our model architecture and data generation pipeline in simulation and find we can achieve @math 90 success rate on previously unseen realistic objects at test time despite having only been trained on random objects. Deep neural nets have caused a revolution in many classification tasks. A related ongoing revolution---also theoretically not understood---concerns their ability to serve as generative models for complicated types of data such as images and texts. These models are trained using ideas like variational autoencoders and Generative Adversarial Networks. We take a first cut at explaining the expressivity of multilayer nets by giving a sufficient criterion for a function to be approximable by a neural network with @math hidden layers. A key ingredient is Barron's Theorem Barron1993 , which gives a Fourier criterion for approximability of a function by a neural network with 1 hidden layer. We show that a composition of @math functions which satisfy certain Fourier conditions ("Barron functions") can be approximated by a @math -layer neural network. For probability distributions, this translates into a criterion for a probability distribution to be approximable in Wasserstein distance---a natural metric on probability distributions---by a neural network applied to a fixed base distribution (e.g., multivariate gaussian). Building up recent lower bound work, we also give an example function that shows that composition of Barron functions is more expressive than Barron functions alone. The Madry Lab recently hosted a competition designed to test the robustness of their adversarially trained MNIST model. Attacks were constrained to perturb each pixel of the input image by a scaled maximal @math distortion @math = 0.3. This discourages the use of attacks which are not optimized on the @math distortion metric. Our experimental results demonstrate that by relaxing the @math constraint of the competition, the elastic-net attack to deep neural networks (EAD) can generate transferable adversarial examples which, despite their high average @math distortion, have minimal visual distortion. These results call into question the use of @math as a sole measure for visual distortion, and further demonstrate the power of EAD at generating robust adversarial examples. A Triangle Generative Adversarial Network ( @math -GAN) is developed for semi-supervised cross-domain joint distribution matching, where the training data consists of samples from each domain, and supervision of domain correspondence is provided by only a few paired samples. @math -GAN consists of four neural networks, two generators and two discriminators. The generators are designed to learn the two-way conditional distributions between the two domains, while the discriminators implicitly define a ternary discriminative function, which is trained to distinguish real data pairs and two kinds of fake data pairs. The generators and discriminators are trained together using adversarial learning. Under mild assumptions, in theory the joint distributions characterized by the two generators concentrate to the data distribution. In experiments, three different kinds of domain pairs are considered, image-label, image-image and image-attribute pairs. Experiments on semi-supervised image classification, image-to-image translation and attribute-based image generation demonstrate the superiority of the proposed approach. A @math -modal probability distribution over the discrete domain @math is one whose histogram has at most @math "peaks" and "valleys." Such distributions are natural generalizations of monotone ( @math ) and unimodal ( @math ) probability distributions, which have been intensively studied in probability theory and statistics. In this paper we consider the problem of (i.e., performing density estimation of) an unknown @math -modal distribution with respect to the @math distance. The learning algorithm is given access to independent samples drawn from an unknown @math -modal distribution @math , and it must output a hypothesis distribution @math such that with high probability the total variation distance between @math and @math is at most @math Our main goal is to obtain algorithms for this problem that use (close to) an information-theoretically optimal number of samples. We give an efficient algorithm for this problem that runs in time @math . For @math , the number of samples used by our algorithm is very close (within an @math factor) to being information-theoretically optimal. Prior to this work computationally efficient algorithms were known only for the cases @math Birge:87b,Birge:97 . A novel feature of our approach is that our learning algorithm crucially uses a new algorithm for as a key subroutine. The learning algorithm uses the property tester to efficiently decompose the @math -modal distribution into @math (near-)monotone distributions, which are easier to learn. Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully applied to learn maps across high-dimensional domains. However, little is known about the nature of the map learned with a GAN objective. To address this problem, we propose a generative adversarial model in which the discriminator's objective is the @math -Wasserstein metric. We show that during training, our generator follows the @math -geodesic between the initial and the target distributions. As a consequence, it reproduces an optimal map at the end of training. We validate our approach empirically in both low-dimensional and high-dimensional continuous settings, and show that it outperforms prior methods on image data. Independent samples from an unknown probability distribution @math on a domain of size @math are distributed across @math players, with each player holding one sample. Each player can communicate @math bits to a central referee in a simultaneous message passing (SMP) model of communication to help the referee infer a property of the unknown @math . When @math bits, the problem reduces to the well-studied collocated case where all the samples are available in one place. In this work, we focus on the communication-starved setting of @math , in which the landscape may change drastically. We propose a general formulation for inference problems in this distributed setting, and instantiate it to two prototypical inference questions: learning and uniformity testing. Brenier's theorem is a cornerstone of optimal transport that guarantees the existence of an optimal transport map @math between two probability distributions @math and @math over @math under certain regularity conditions. The main goal of this work is to establish the minimax rates estimation rates for such a transport map from data sampled from @math and @math under additional smoothness assumptions on @math . To achieve this goal, we develop an estimator based on the minimization of an empirical version of the semi-dual optimal transport problem, restricted to truncated wavelet expansions. This estimator is shown to achieve near minimax optimality using new stability arguments for the semi-dual and a complementary minimax lower bound. These are the first minimax estimation rates for transport maps in general dimension. We present two classes of improved estimators for mutual information @math , from samples of random points distributed according to some joint probability density @math . In contrast to conventional estimators based on binnings, they are based on entropy estimates from @math -nearest neighbor distances. This means that they are data efficient (with @math we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to nonuniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of @math for @math points. Numerically, we find that both families become exact for independent distributions, i.e. the estimator @math vanishes (up to statistical fluctuations) if @math . This holds for all tested marginal distributions and for all dimensions of @math and @math . In addition, we give estimators for redundancies between more than two random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation. The advent of deep learning is a breakthrough in artificial intelligence, for which a theoretical understanding is lacking. Supervised deep learning involves the training of neural networks with a large number @math of parameters. For large enough @math , in the so-called over-parametrized regime, one can essentially fit the training data points. Sparsity-based arguments would suggest that the generalization error increases as @math grows past a certain threshold @math . Instead, empirical studies have shown that in the over-parametrized regime, generalization error keeps decreasing with @math . We resolve this paradox, through a new framework. We rely on the so-called Neural Tangent Kernel, which connects large neural nets to kernel methods, to show that the initialization causes finite-size random fluctuations @math of the neural net output function @math around its expectation @math . These affect the generalization error @math for classification: under natural assumptions, it decays to a plateau value @math in a power-law fashion @math . This description breaks down at a so-called jamming transition @math . At this threshold, we argue that @math diverges. This result leads to a plausible explanation for the cusp in test error known to occur at @math . Our results are confirmed by extensive empirical observations on the MNIST and CIFAR image datasets. Our analysis finally suggests that, given a computational envelope, it is best to use several nets of intermediate sizes, just beyond @math , and to average their outputs. We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . With the development of deep learning, supervised learning has frequently been adopted to classify remotely sensed images using convolutional networks. However, due to the limited amount of labeled data available, supervised learning is often difficult to carry out. Therefore, we proposed an unsupervised model called multiple-layer feature-matching generative adversarial networks (MARTA GANs) to learn a representation using only unlabeled data. MARTA GANs consists of both a generative model @math and a discriminative model @math . We treat @math as a feature extractor. To fit the complex properties of remote sensing data, we use a fusion layer to merge the mid-level and global features. @math can produce numerous images that are similar to the training data; therefore, @math can learn better representations of remotely sensed images using the training data provided by @math . The classification results on two widely used remote sensing image databases show that the proposed method significantly improves the classification performance compared with other state-of-the-art methods. This paper proposes the novel Pose Guided Person Generation Network (PG @math ) that allows to synthesize person images in arbitrary poses, based on an image of that person and a novel pose. Our generation framework PG @math utilizes the pose information explicitly and consists of two key stages: pose integration and image refinement. In the first stage the condition image and the target pose are fed into a U-Net-like network to generate an initial but coarse image of the person with the target pose. The second stage then refines the initial and blurry result by training a U-Net-like generator in an adversarial way. Extensive experimental results on both 128 @math 64 re-identification images and 256 @math 256 fashion photos show that our model generates high-quality person images with convincing details. We consider linear regression in the high-dimensional regime where the number of observations @math is smaller than the number of parameters @math . A very successful approach in this setting uses @math -penalized least squares (a.k.a. the Lasso) to search for a subset of @math parameters that best explain the data, while setting the other parameters to zero. Considerable amount of work has been devoted to characterizing the estimation and model selection problems within this approach. In this paper we consider instead the fundamental, but far less understood, question of . More precisely, we address the problem of computing p-values for single regression coefficients. On one hand, we develop a general upper bound on the minimax power of tests with a given significance level. On the other, we prove that this upper bound is (nearly) achievable through a practical procedure in the case of random design matrices with independent entries. Our approach is based on a debiasing of the Lasso estimator. The analysis builds on a rigorous characterization of the asymptotic distribution of the Lasso estimator and its debiased version. Our result holds for optimal sample size, i.e., when @math is at least on the order of @math . We generalize our approach to random design matrices with i.i.d. Gaussian rows @math . In this case we prove that a similar distributional characterization (termed standard distributional limit') holds for @math much larger than @math . Finally, we show that for optimal sample size, @math being at least of order @math , the standard distributional limit for general Gaussian designs can be derived from the replica heuristics in statistical physics. A new form of variational autoencoder (VAE) is developed, in which the joint distribution of data and codes is considered in two (symmetric) forms: ( @math ) from observed data fed through the encoder to yield codes, and ( @math ) from latent codes drawn from a simple prior and propagated through the decoder to manifest data. Lower bounds are learned for marginal log-likelihood fits observed data and latent codes. When learning with the variational bound, one seeks to minimize the symmetric Kullback-Leibler divergence of joint density functions from ( @math ) and ( @math ), while simultaneously seeking to maximize the two marginal log-likelihoods. To facilitate learning, a new form of adversarial training is developed. An extensive set of experiments is performed, in which we demonstrate state-of-the-art data reconstruction and generation on several image benchmark datasets. Adversarial attacks involve adding, small, often imperceptible, perturbations to inputs with the goal of getting a machine learning model to misclassifying them. While many different adversarial attack strategies have been proposed on image classification models, object detection pipelines have been much harder to break. In this paper, we propose a novel strategy to craft adversarial examples by solving a constrained optimization problem using an adversarial generator network. Our approach is fast and scalable, requiring only a forward pass through our trained generator network to craft an adversarial sample. Unlike in many attack strategies, we show that the same trained generator is capable of attacking new images without explicitly optimizing on them. We evaluate our attack on a trained Faster R-CNN face detector on the cropped 300-W face dataset where we manage to reduce the number of detected faces to @math of all originally detected faces. In a different experiment, also on 300-W, we demonstrate the robustness of our attack to a JPEG compression based defense typical JPEG compression level of @math reduces the effectiveness of our attack from only @math of detected faces to a modest @math . Recent studies have highlighted the vulnerability of deep neural networks (DNNs) to adversarial examples - a visually indistinguishable adversarial image can easily be crafted to cause a well-trained model to misclassify. Existing methods for crafting adversarial examples are based on @math and @math distortion metrics. However, despite the fact that @math distortion accounts for the total variation and encourages sparsity in the perturbation, little has been developed for crafting @math -based adversarial examples. In this paper, we formulate the process of attacking DNNs via adversarial examples as an elastic-net regularized optimization problem. Our elastic-net attacks to DNNs (EAD) feature @math -oriented adversarial examples and include the state-of-the-art @math attack as a special case. Experimental results on MNIST, CIFAR10 and ImageNet show that EAD can yield a distinct set of adversarial examples with small @math distortion and attains similar attack performance to the state-of-the-art methods in different attack scenarios. More importantly, EAD leads to improved attack transferability and complements adversarial training for DNNs, suggesting novel insights on leveraging @math distortion in adversarial machine learning and security implications of DNNs. We study the problem of estimating a set of @math linear queries with respect to some unknown distribution @math over a domain @math based on a sensitive data set of @math individuals under the constraint of local differential privacy. This problem subsumes a wide range of estimation tasks, e.g., distribution estimation and @math -dimensional mean estimation. We provide new algorithms for both the offline (non-adaptive) and adaptive versions of this problem. In the offline setting, the set of queries are fixed before the algorithm starts. In the regime where @math , our algorithms attain @math estimation error that is independent of @math , and is tight up to a factor of @math . For the special case of distribution estimation, we show that projecting the output estimate of an algorithm due to [ 2018] on the probability simplex yields an @math error that depends only sub-logarithmically on @math in the regime where @math . These results show the possibility of accurate estimation of linear queries in the high-dimensional settings under the @math error criterion. In the adaptive setting, the queries are generated over @math rounds; one query at a time. In each round, a query can be chosen adaptively based on all the history of previous queries and answers. We give an algorithm for this problem with optimal @math estimation error (worst error in the estimated values for the queries w.r.t. the data distribution). Our bound matches a lower bound on the @math error for the offline version of this problem [ 2013]. We study the flow of information and the evolution of internal representations during deep neural network (DNN) training, aiming to demystify the compression aspect of the information bottleneck theory. The theory suggests that DNN training comprises a rapid fitting phase followed by a slower compression phase, in which the mutual information @math between the input @math and internal representations @math decreases. Several papers observe compression of estimated mutual information on different DNN models, but the true @math over these networks is provably either constant (discrete @math ) or infinite (continuous @math ). This work explains the discrepancy between theory and experiments, and clarifies what was actually measured by these past works. To this end, we introduce an auxiliary (noisy) DNN framework for which @math is a meaningful quantity that depends on the network's parameters. This noisy framework is shown to be a good proxy for the original (deterministic) DNN both in terms of performance and the learned representations. We then develop a rigorous estimator for @math in noisy DNNs and observe compression in various models. By relating @math in the noisy DNN to an information-theoretic communication problem, we show that compression is driven by the progressive clustering of hidden representations of inputs from the same class. Several methods to directly monitor clustering of hidden representations, both in noisy and deterministic DNNs, are used to show that meaningful clusters form in the @math space. Finally, we return to the estimator of @math employed in past works, and demonstrate that while it fails to capture the true (vacuous) mutual information, it does serve as a measure for clustering. This clarifies the past observations of compression and isolates the geometric clustering of hidden representations as the true phenomenon of interest.