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In this paper, we study the problem of multitask metric learning (mtML). We first examine the generalization bound of the regularized mtML f… (see more)ormulation based on the notion of algorithmic stability, proving the convergence rate of mtML and revealing the trade-off between the tasks. Moreover, we also establish the theoretical connection between the mtML, single-task learning and pooling-task learning approaches. In addition, we present a novel boosting-based mtML (mt-BML) algorithm, which scales well with the feature dimension of the data. Finally, we also devise an efficient second-order Riemannian retraction operator which is tailored specifically to our mt-BML algorithm. It produces a low-rank solution of mtML to reduce the model complexity, and may also improve generalization performances. Extensive evaluations on several benchmark data sets verify the effectiveness of our learning algorithm.
2019-04-11
International Conference on Artificial Intelligence and Statistics (published)
Games generalize the single-objective optimization paradigm by introducing different objective functions for different players. Differentiab… (see more)le games often proceed by simultaneous or alternating gradient updates. In machine learning, games are gaining new importance through formulations like generative adversarial networks (GANs) and actor-critic systems. However, compared to single-objective optimization, game dynamics are more complex and less understood. In this paper, we analyze gradient-based methods with momentum on simple games. We prove that alternating updates are more stable than simultaneous updates. Next, we show both theoretically and empirically that alternating gradient updates with a negative momentum term achieves convergence in a difficult toy adversarial problem, but also on the notoriously difficult to train saturating GANs.
2019-04-11
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics (published)
Imitation learning is an effective alternative approach to learn a policy when the reward function is sparse. In this paper, we consider a c… (see more)hallenging setting where an agent and an expert use different actions from each other. We assume that the agent has access to a sparse reward function and state-only expert observations. We propose a method which gradually balances between the imitation learning cost and the reinforcement learning objective. In addition, this method adapts the agent's policy based on either mimicking expert behavior or maximizing sparse reward. We show, through navigation scenarios, that (i) an agent is able to efficiently leverage sparse rewards to outperform standard state-only imitation learning, (ii) it can learn a policy even when its actions are different from the expert, and (iii) the performance of the agent is not bounded by that of the expert, due to the optimized usage of sparse rewards.
In recent years, multi-armed bandit (MAB) framework has attracted a lot of attention in various applications, from recommender systems and i… (see more)nformation retrieval to healthcare and finance, due to its stellar performance combined with certain attractive properties, such as learning from less feedback. The multi-armed bandit field is currently flourishing, as novel problem settings and algorithms motivated by various practical applications are being introduced, building on top of the classical bandit problem. This article aims to provide a comprehensive review of top recent developments in multiple real-life applications of the multi-armed bandit. Specifically, we introduce a taxonomy of common MAB-based applications and summarize state-of-art for each of those domains. Furthermore, we identify important current trends and provide new perspectives pertaining to the future of this exciting and fast-growing field.
We present a novel recurrent neural network (RNN)–based model that combines the remembering ability of unitary evolution RNNs with the abi… (see more)lity of gated RNNs to effectively forget redundant or irrelevant information in its memory. We achieve this by extending restricted orthogonal evolution RNNs with a gating mechanism similar to gated recurrent unit RNNs with a reset gate and an update gate. Our model is able to outperform long short-term memory, gated recurrent units, and vanilla unitary or orthogonal RNNs on several long-term-dependency benchmark tasks. We empirically show that both orthogonal and unitary RNNs lack the ability to forget. This ability plays an important role in RNNs. We provide competitive results along with an analysis of our model on many natural sequential tasks, including question answering, speech spectrum prediction, character-level language modeling, and synthetic tasks that involve long-term dependencies such as algorithmic, denoising, and copying tasks.
Motivated by estimation problems arising in autonomous vehicles and decentralized control of unmanned aerial vehicles, we consider multi-age… (see more)nt estimation and filtering problems in which multiple agents generate state estimates based on decentralized information and the objective is to minimize a coupled mean-squared error which we call team mean-square error. We call the resulting estimates as minimum team mean-squared error (MTMSE) estimates. We show that MTMSE estimates are different from minimum mean-squared error (MMSE) estimates. We derive closed-form expressions for MTMSE estimates, which are linear function of the observations where the corresponding gain depends on the weight matrix that couples the estimation error. We then consider a filtering problem where a linear stochastic process is monitored by multiple agents which can share their observations (with delay) over a communication graph. We derive expressions to recursively compute the MTMSE estimates. To illustrate the effectiveness of the proposed scheme we consider an example of estimating the distances between vehicles in a platoon and show that MTMSE estimates significantly outperform MMSE estimates and consensus Kalman filtering estimates.
This paper provides a taxonomy for the licensing of data in the fields of artificial intelligence and machine learning. The paper's goal is … (see more)to build towards a common framework for data licensing akin to the licensing of open source software. Increased transparency and resolving conceptual ambiguities in existing licensing language are two noted benefits of the approach proposed in the paper. In parallel, such benefits may help foster fairer and more efficient markets for data through bringing about clearer tools and concepts that better define how data can be used in the fields of AI and ML. The paper's approach is summarized in a new family of data license language - \textit{the Montreal Data License (MDL)}. Alongside this new license, the authors and their collaborators have developed a web-based tool to generate license language espousing the taxonomies articulated in this paper.
Continual learning is the ability of an agent to learn online with a non-stationary and never-ending stream of data. A key component for suc… (see more)h never-ending learning process is to overcome the catastrophic forgetting of previously seen data, a problem that neural networks are well known to suffer from. The solutions developed so far often relax the problem of continual learning to the easier task-incremental setting, where the stream of data is divided into tasks with clear boundaries. In this paper, we break the limits and move to the more challenging online setting where we assume no information of tasks in the data stream. We start from the idea that each learning step should not increase the losses of the previously learned examples through constraining the optimization process. This means that the number of constraints grows linearly with the number of examples, which is a serious limitation. We develop a solution to select a fixed number of constraints that we use to approximate the feasible region defined by the original constraints. We compare our approach against the methods that rely on task boundaries to select a fixed set of examples, and show comparable or even better results, especially when the boundaries are blurry or when the data distributions are imbalanced.
Abstract Large-scale in vivo neuroimaging datasets offer new possibilities for reliable, well-powered measures of interregional structural d… (see more)ifferences and biomarkers of pathological changes in a wide variety of neurological and psychiatric diseases. However, so far studies have been structurally and functionally imprecise, being unable to relate pathological changes to specific cortical layers or neurobiological processes. We developed artificial neural networks to segment cortical and laminar surfaces in the BigBrain, a 3D histological model of the human brain. We sought to test whether previously-reported thickness gradients, as measured by MRI, in sensory and motor processing cortices, were present in a histological atlas of cortical thickness, and which cortical layers were contributing to these gradients. Identifying common gradients of cortical organisation enables us to meaningfully relate microstructural, macrostructural and functional cortical parameters. Analysis of thickness gradients across sensory cortices, using our fully segmented six-layered model, was consistent with MRI findings, showing increasing thickness moving up the processing hierarchy. In contrast, fronto-motor cortices showed the opposite pattern with changes in thickness of layers III, V and VI being the primary drivers of these gradients. As well as identifying key differences between sensory and motor gradients, our findings show how the use of this laminar atlas offers insights that will be key to linking single-neuron morphological changes, mesoscale cortical layers and macroscale cortical thickness.
Histological atlases of the cerebral cortex, such as those made famous by Brodmann and von Economo, are invaluable for understanding human b… (see more)rain microstructure and its relationship with functional organization in the brain. However, these existing atlases are limited to small numbers of manually annotated samples from a single cerebral hemisphere, measured from 2D histological sections. We present the first whole-brain quantitative 3D laminar atlas of the human cerebral cortex. This atlas was derived from a 3D histological model of the human brain at 20 micron isotropic resolution (BigBrain), using a convolutional neural network to segment, automatically, the cortical layers in both hemispheres. Our approach overcomes many of the historical challenges with measurement of histological thickness in 2D and the resultant laminar atlas provides an unprecedented level of precision and detail. We utilized this BigBrain cortical atlas to test whether previously reported thickness gradients, as measured by MRI in sensory and motor processing cortices, were present in a histological atlas of cortical thickness, and which cortical layers were contributing to these gradients. Cortical thickness increased across sensory processing hierarchies, primarily driven by layers III, V and VI. In contrast, fronto-motor cortices showed the opposite pattern, with decreases in total and pyramidal layer thickness. These findings illustrate how this laminar atlas will provide a link between single-neuron morphology, mesoscale cortical layering, macroscopic cortical thickness and, ultimately, functional neuroanatomy.
LF-PPL: A Low-Level First Order Probabilistic Programming Language for Non-Differentiable Models
Yuanshuo Zhou
Bradley Gram-Hansen
Tobias Kohn
Tom Rainforth
Hongseok Yang
Frank Wood
We develop a new Low-level, First-order Probabilistic Programming Language~(LF-PPL) suited for models containing a mix of continuous, discre… (see more)te, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density function is discontinuous with respect to, while further providing runtime checks for boundary crossings. This enables the introduction of new inference engines that are able to exploit gradient information, while remaining efficient for models which are not everywhere differentiable. We demonstrate this ability by incorporating a discontinuous Hamiltonian Monte Carlo (DHMC) inference
engine that is able to deliver automated and efficient inference for non-differentiable models. Our system is backed up by a mathematical formalism that ensures that any model expressed in this language has a density with measure zero discontinuities to maintain the validity of the inference engine.
