We introduce a pretraining technique called Selfie, which stands for SELF-supervised Image Embedding. Selfie generalizes the concept of masked language modeling to continuous data, such as images. Given masked-out patches in an input image, our method learns to select the correct patch, among other "distractor" patches sampled from the same image, to fill in the masked location. This classification objective sidesteps the need for predicting exact pixel values of the target patches. The pretraining architecture includes a network of convolutional blocks to process patches followed by an attention pooling network to summarize the content of unmasked patches before predicting masked ones. During finetuning, we reuse the convolutional weights found by pretraining. We evaluate our method on three benchmarks (CIFAR-10, ImageNet 32 x 32, and ImageNet 224 x 224) with varying amounts of labeled data, from 5% to 100% of the training sets. Our pretraining method provides consistent improvements to ResNet-50 across all settings compared to the standard supervised training of the same network. Notably, on ImageNet 224 x 224 with 60 examples per class (5%), our method improves the mean accuracy of ResNet-50 from 35.6% to 46.7%, an improvement of 11.1 points in absolute accuracy. Our pretraining method also improves ResNet-50 training stability, especially on low data regime, by significantly lowering the standard deviation of test accuracies across datasets.

Classifier chains have recently been proposed as an appealing method for tackling the multi-label classification task. In addition to several empirical studies showing its state-of-the-art performance, especially when being used in its ensemble variant, there are also some first results on theoretical properties of classifier chains. Continuing along this line, we analyze the influence of a potential pitfall of the learning process, namely the discrepancy between the feature spaces used in training and testing: While true class labels are used as supplementary attributes for training the binary models along the chain, the same models need to rely on estimations of these labels at prediction time. We elucidate under which circumstances the attribute noise thus created can affect the overall prediction performance. As a result of our findings, we propose two modifications of classifier chains that are meant to overcome this problem. Experimentally, we show that our variants are indeed able to produce better results in cases where the original chaining process is likely to fail.

How many training data are needed to learn a supervised task? It is often observed that the generalization error decreases as $n^{-\beta}$ where $n$ is the number of training examples and $\beta$ an exponent that depends on both data and algorithm. In this work we measure $\beta$ when applying kernel methods to real datasets. For MNIST we find $\beta\approx 0.4$ and for CIFAR10 $\beta\approx 0.1$. Remarkably, $\beta$ is the same for regression and classification tasks, and for Gaussian or Laplace kernels. To rationalize the existence of non-trivial exponents that can be independent of the specific kernel used, we introduce the Teacher-Student framework for kernels. In this scheme, a Teacher generates data according to a Gaussian random field, and a Student learns them via kernel regression. With a simplifying assumption --- namely that the data are sampled from a regular lattice --- we derive analytically $\beta$ for translation invariant kernels, using previous results from the kriging literature. Provided that the Student is not too sensitive to high frequencies, $\beta$ depends only on the training data and their dimension. We confirm numerically that these predictions hold when the training points are sampled at random on a hypersphere. Overall, our results quantify how smooth Gaussian data should be to avoid the curse of dimensionality, and indicate that for kernel learning the relevant dimension of the data should be defined in terms of how the distance between nearest data points depends on $n$. With this definition one obtains reasonable effective smoothness estimates for MNIST and CIFAR10.

You see that the model makes reasonably accurate predictions, with the exception of one wrong classification in row 29, where "Versicolor" was predicted while the test label is "Virginica". This is already some indication of your model's performance, but you might want to go even deeper into your analysis.

Structured prediction can be considered as a generalization of many standard supervised learning tasks, and is usually thought as a simultaneous prediction of multiple labels. One standard approach is to maximize a score function on the space of labels, which decomposes as a sum of unary and pairwise potentials, each depending on one or two specific labels, respectively. For this approach, several learning and inference algorithms have been proposed over the years, ranging from exact to approximate methods while balancing the computational complexity. However, in contrast to binary and multiclass classification, results on the necessary number of samples for achieving learning is still limited, even for a specific family of predictors such as factor graphs. In this work, we provide minimax bounds for a class of factor-graph inference models for structured prediction. That is, we characterize the necessary sample complexity for any conceivable algorithm to achieve learning of factor-graph predictors.

Structured prediction can be thought of as a simultaneous prediction of multiple labels. This is often done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise and unary potentials. The above is naturally modeled with a graph, where edges and vertices are related to pairwise and unary potentials, respectively. We consider the generative process proposed by Globerson et al. and apply it to general connected graphs. We analyze the structural conditions of the graph that allow for the exact recovery of the labels. Our results show that exact recovery is possible and achievable in polynomial time for a large class of graphs. In particular, we show that graphs that are bad expanders can be exactly recovered by adding small edge perturbations coming from the Erd\H{o}s-R\'enyi model. Finally, as a byproduct of our analysis, we provide an extension of Cheeger's inequality.

Partial Label Learning (PLL) aims to learn from the data where each training instance is associated with a set of candidate labels, among which only one is correct. Most existing methods deal with such problem by either treating each candidate label equally or identifying the ground-truth label iteratively. In this paper, we propose a novel PLL approach called HERA, which simultaneously incorporates the HeterogEneous Loss and the SpaRse and Low-rAnk procedure to estimate the labeling confidence for each instance while training the model. Specifically, the heterogeneous loss integrates the strengths of both the pairwise ranking loss and the pointwise reconstruction loss to provide informative label ranking and reconstruction information for label identification, while the embedded sparse and low-rank scheme constrains the sparsity of ground-truth label matrix and the low rank of noise label matrix to explore the global label relevance among the whole training data for improving the learning model. Extensive experiments on both artificial and real-world data sets demonstrate that our method can achieve superior or comparable performance against the state-of-the-art methods.

In this paper, we propose a general framework for using adversarial label learning (ALL) [1] for multiclass classification when the data is weakly supervised. We introduce a new variant of ALL that incorporates human knowledge through multiple constraint types. Like adversarial label learning, we learn by adversarially finding labels constrained to be partially consistent with the weak supervision. However, we describe a different approach to solve the optimization that enjoys faster convergence when training large deep models. Our framework allows for human knowledge to be encoded into the algorithm as a set of linear constraints. We then solve a two-player game optimization subject to these constraints. We test our method on three data sets by training convolutional neural network models that learn to classify image objects with limited access to training labels. Our approach is able to learn even in settings where the weak supervision confounds state-of-the-art weakly supervised learning methods. The results of our experiments demonstrate the applicability of this approach to general classification tasks.

In this paper, we aim to recover the 3D human pose from 2D body joints of a single image. The major challenge in this task is the depth ambiguity since different 3D poses may produce similar 2D poses. Although many recent advances in this problem are found in both unsupervised and supervised learning approaches, the performances of most of these approaches are greatly affected by insufficient diversities and richness of training data. To alleviate this issue, we propose an unsupervised learning approach, which is capable of estimating various complex poses well under limited available training data. Specifically, we propose a Shape Decomposition Model (SDM) in which a 3D pose is considered as the superposition of two parts which are global structure together with some deformations. Based on SDM, we estimate these two parts explicitly by solving two sets of different distributed combination coefficients of geometric priors. In addition, to obtain geometric priors, a joint dictionary learning algorithm is proposed to extract both coarse and fine pose clues simultaneously from limited training data. Quantitative evaluations on several widely used datasets demonstrate that our approach yields better performances over other competitive approaches. Especially, on some categories with more complex deformations, significant improvements are achieved by our approach. Furthermore, qualitative experiments conducted on in-the-wild images also show the effectiveness of the proposed approach.