We present a novel framework, called GRAB (GRaphical models with overlApping Blocks), to capture densely connected components in a network estimate. GRAB takes as input a data matrix of p variables and n samples, and jointly learns both a network among p variables and densely connected groups of variables (called `blocks'). GRAB has four major novelties as compared to existing network estimation methods: 1) It does not require the blocks to be given a priori.

Deep metric learning has gained much popularity in recent years, following the success of deep learning. However, existing frameworks of deep metric learning based on contrastive loss and triplet loss often suffer from slow convergence, partially because they employ only one negative example while not interacting with the other negative classes in each update. In this paper, we propose to address this problem with a new metric learning objective called multi-class N-pair loss. The proposed objective function firstly generalizes triplet loss by allowing joint comparison among more than one negative examples - more specifically, N-1 negative examples - and secondly reduces the computational burden of evaluating deep embedding vectors via an efficient batch construction strategy using only N pairs of examples, instead of (N+1) N. We demonstrate the superiority of our proposed loss to the triplet loss as well as other competing loss functions for a variety of tasks on several visual recognition benchmark, including fine-grained object recognition and verification, image clustering and retrieval, and face verification and identification.

Variational autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared to the purely bottom-up inference in layered Variational Autoencoders and other generative models. We provide a detailed analysis of the learned hierarchical latent representation and show that our new inference model is qualitatively different and utilizes a deeper more distributed hierarchy of latent variables. Finally, we observe that batch-normalization and deterministic warm-up (gradually turning on the KL-term) are crucial for training variational models with many stochastic layers.

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior over parameters by conditioning on data being inside an ε-ball around the observed data, which is only correct in the limit ε 0. Monte Carlo methods can then draw samples from the approximate posterior to approximate predictions or error bars on parameters.

We propose a criterion for discrimination against a specified sensitive attribute in supervised learning, where the goal is to predict some target based on available features. Assuming data about the predictor, target, and membership in the protected group are available, we show how to optimally adjust any learned predictor so as to remove discrimination according to our definition. Our framework also improves incentives by shifting the cost of poor classification from disadvantaged groups to the decision maker, who can respond by improving the classification accuracy.

This paper presents Generalized Correspondence-LDA (GC-LDA), a generalization of the Correspondence-LDA model that allows for variable spatial representations to be associated with topics, and increased flexibility in terms of the strength of the correspondence between data types induced by the model. We present three variants of GC-LDA, each of which associates topics with a different spatial representation, and apply them to a corpus of neuroimaging data. In the context of this dataset, each topic corresponds to a functional brain region, where the region's spatial extent is captured by a probability distribution over neural activity, and the region's cognitive function is captured by a probability distribution over linguistic terms. We illustrate the qualitative improvements offered by GC-LDA in terms of the types of topics extracted with alternative spatial representations, as well as the model's ability to incorporate a-priori knowledge from the neuroimaging literature. We furthermore demonstrate that the novel features of GC-LDA improve predictions for missing data.

The recursive teaching dimension (RTD) of a concept class $C \subseteq \{0, 1\}^n$, introduced by Zilles et al. [ZLHZ11], is a complexity parameter measured by the worst-case number of labeled examples needed to learn any target concept of $C$ in the recursive teaching model. In this paper, we study the quantitative relation between RTD and the well-known learning complexity measure VC dimension (VCD), and improve the best known upper and (worst-case) lower bounds on the recursive teaching dimension with respect to the VC dimension. Given a concept class $C \subseteq \{0, 1\}^n$ with $VCD(C) = d$, we first show that $RTD(C)$ is at most $d 2^{d+1}$. This is the first upper bound for $RTD(C)$ that depends only on $VCD(C)$, independent of the size of the concept class $|C|$ and its~domain size $n$.

Generative state estimators based on probabilistic filters and smoothers are one of the most popular classes of state estimators for robots and autonomous vehicles. However, generative models have limited capacity to handle rich sensory observations, such as camera images, since they must model the entire distribution over sensor readings. Discriminative models do not suffer from this limitation, but are typically more complex to train as latent variable models for state estimation. We present an alternative approach where the parameters of the latent state distribution are directly optimized as a deterministic computation graph, resulting in a simple and effective gradient descent algorithm for training discriminative state estimators. We show that this procedure can be used to train state estimators that use complex input, such as raw camera images, which must be processed using expressive nonlinear function approximators such as convolutional neural networks. Our model can be viewed as a type of recurrent neural network, and the connection to probabilistic filtering allows us to design a network architecture that is particularly well suited for state estimation. We evaluate our approach on synthetic tracking task with raw image inputs and on the visual odometry task in the KITTI dataset. The results show significant improvement over both standard generative approaches and regular recurrent neural networks.

We study the problem of learning influence functions under incomplete observations of node activations. Incomplete observations are a major concern as most (online and real-world) social networks are not fully observable. We establish both proper and improper PAC learnability of influence functions under randomly missing observations. Proper PAC learnability under the Discrete-Time Linear Threshold (DLT) and Discrete-Time Independent Cascade (DIC) models is established by reducing incomplete observations to complete observations in a modified graph. Our improper PAC learnability result applies for the DLT and DIC models as well as the Continuous-Time Independent Cascade (CIC) model. It is based on a parametrization in terms of reachability features, and also gives rise to an efficient and practical heuristic. Experiments on synthetic and real-world datasets demonstrate the ability of our method to compensate even for a fairly large fraction of missing observations.

Binary hashing is a well-known approach for fast approximate nearest-neighbor search in information retrieval. Much work has focused on affinity-based objective functions involving the hash functions or binary codes. These objective functions encode neighborhood information between data points and are often inspired by manifold learning algorithms. They ensure that the hash functions differ from each other through constraints or penalty terms that encourage codes to be orthogonal or dissimilar across bits, but this couples the binary variables and complicates the already difficult optimization. We propose a much simpler approach: we train each hash function (or bit) independently from each other, but introduce diversity among them using techniques from classifier ensembles. Surprisingly, we find that not only is this faster and trivially parallelizable, but it also improves over the more complex, coupled objective function, and achieves state-of-the-art precision and recall in experiments with image retrieval.