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We introduce the Neural Conditioner (NC), a self-supervised machine able to learn about all the conditional distributions of a random vector $X$. The NC is a function $NC(x cdot a, a, r)$ that leverages adversarial training to match each conditional distribution $P(X_r|X_a=x_a)$. After training, the NC generalizes to sample from conditional distributions never seen, including the joint distribution. The NC is also able to auto-encode examples, providing data representations useful for downstream classification tasks. In sum, the NC integrates different self-supervised tasks (each being the estimation of a conditional distribution) and levels of supervision (partially observed data) seamlessly into a single learning experience.
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Many machine learning tasks, such as learning with invariance and policy evaluation in reinforcement learning, can be characterized as problems of learning from conditional distributions. In such problems, each sample $x$ itself is associated with a conditional distribution $p(z|x)$ represented by samples ${z_i}_{i=1}^M$, and the goal is to learn a function $f$ that links these conditional distributions to target values $y$. These learning problems become very challenging when we only have limited samples or in the extreme case only one sample from each conditional distribution. Commonly used approaches either assume that $z$ is independent of $x$, or require an overwhelmingly large samples from each conditional distribution. To address these challenges, we propose a novel approach which employs a new min-max reformulation of the learning from conditional distribution problem. With such new reformulation, we only need to deal with the joint distribution $p(z,x)$. We also design an efficient learning algorithm, Embedding-SGD, and establish theoretical sample complexity for such problems. Finally, our numerical experiments on both synthetic and real-world datasets show that the proposed approach can significantly improve over the existing algorithms.
We propose networked exponential families to jointly leverage the information in the topology as well as the attributes (features) of networked data points. Networked exponential families are a flexible probabilistic model for heterogeneous datasets with intrinsic network structure. These models can be learnt efficiently using network Lasso which implicitly pools or clusters the data points according to the intrinsic network structure and the local likelihood. The resulting method can be formulated as a non-smooth convex optimization problem which we solve using a primal-dual splitting method. This primal-dual method is appealing for big data applications as it can be implemented as a highly scalable message passing algorithm.
The principal contribution of this paper is a conceptual framework for off-policy reinforcement learning, based on conditional expectations of importance sampling ratios. This framework yields new perspectives and understanding of existing off-policy algorithms, and reveals a broad space of unexplored algorithms. We theoretically analyse this space, and concretely investigate several algorithms that arise from this framework.
Recent methods for learning unsupervised visual representations, dubbed contrastive learning, optimize the noise-contrastive estimation (NCE) bound on mutual information between two views of an image. NCE uses randomly sampled negative examples to normalize the objective. In this paper, we show that choosing difficult negatives, or those more similar to the current instance, can yield stronger representations. To do this, we introduce a family of mutual information estimators that sample negatives conditionally -- in a ring around each positive. We prove that these estimators lower-bound mutual information, with higher bias but lower variance than NCE. Experimentally, we find our approach, applied on top of existing models (IR, CMC, and MoCo) improves accuracy by 2-5% points in each case, measured by linear evaluation on four standard image datasets. Moreover, we find continued benefits when transferring features to a variety of new image distributions from the Meta-Dataset collection and to a variety of downstream tasks such as object detection, instance segmentation, and keypoint detection.
We introduce a general framework for approximating regular conditional distributions (RCDs). Our approximations of these RCDs are implemented by a new class of geometric deep learning models with inputs in $mathbb{R}^d$ and outputs in the Wasserstein-$1$ space $mathcal{P}_1(mathbb{R}^D)$. We find that the models built using our framework can approximate any continuous functions from $mathbb{R}^d$ to $mathcal{P}_1(mathbb{R}^D)$ uniformly on compacts, and quantitative rates are obtained. We identify two methods for avoiding the curse of dimensionality; i.e.: the number of parameters determining the approximating neural network depends only polynomially on the involved dimension and the approximation error. The first solution describes functions in $C(mathbb{R}^d,mathcal{P}_1(mathbb{R}^D))$ which can be efficiently approximated on any compact subset of $mathbb{R}^d$. Conversely, the second approach describes sets in $mathbb{R}^d$, on which any function in $C(mathbb{R}^d,mathcal{P}_1(mathbb{R}^D))$ can be efficiently approximated. Our framework is used to obtain an affirmative answer to the open conjecture of Bishop (1994); namely: mixture density networks are universal regular conditional distributions. The predictive performance of the proposed models is evaluated against comparable learning models on various probabilistic predictions tasks in the context of ELMs, model uncertainty, and heteroscedastic regression. All the results are obtained for more general input and output spaces and thus apply to geometric deep learning contexts.
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