Meta-learning is a framework for learning learning algorithms through repeated interactions with an environment as opposed to designing them by hand. In recent years, this framework has established itself as a promising tool for building models of human cognition. Yet, a coherent research program around meta-learned models of cognition is still missing. The purpose of this article is to synthesize previous work in this field and establish such a research program. We rely on three key pillars to accomplish this goal. We first point out that meta-learning can be used to construct Bayes-optimal learning algorithms. This result not only implies that any behavioral phenomenon that can be explained by a Bayesian model can also be explained by a meta-learned model but also allows us to draw strong connections to the rational analysis of cognition. We then discuss several advantages of the meta-learning framework over traditional Bayesian methods. In particular, we argue that meta-learning can be applied to situations where Bayesian inference is impossible and that it enables us to make rational models of cognition more realistic, either by incorporating limited computational resources or neuroscientific knowledge. Finally, we reexamine prior studies from psychology and neuroscience that have applied meta-learning and put them into the context of these new insights. In summary, our work highlights that meta-learning considerably extends the scope of rational analysis and thereby of cognitive theories more generally.

We propose a hierarchical tensor-network approach for approximating high-dimensional probability density via empirical distribution. This leverages randomized singular value decomposition (SVD) techniques and involves solving linear equations for tensor cores in this tensor network. The complexity of the resulting algorithm scales linearly in the dimension of the high-dimensional density. An analysis of estimation error demonstrates the effectiveness of this method through several numerical experiments.

No free lunch theorems for supervised learning state that no learner can solve all problems or that all learners achieve exactly the same accuracy on average over a uniform distribution on learning problems. Accordingly, these theorems are often referenced in support of the notion that individual problems require specially tailored inductive biases. While virtually all uniformly sampled datasets have high complexity, real-world problems disproportionately generate low-complexity data, and we argue that neural network models share this same preference, formalized using Kolmogorov complexity. Notably, we show that architectures designed for a particular domain, such as computer vision, can compress datasets on a variety of seemingly unrelated domains. Our experiments show that pre-trained and even randomly initialized language models prefer to generate low-complexity sequences. Whereas no free lunch theorems seemingly indicate that individual problems require specialized learners, we explain how tasks that often require human intervention such as picking an appropriately sized model when labeled data is scarce or plentiful can be automated into a single learning algorithm. These observations justify the trend in deep learning of unifying seemingly disparate problems with an increasingly small set of machine learning models.

How to behave efficiently and flexibly is a central problem for understanding biological agents and creating intelligent embodied AI. It has been well known that behavior can be classified as two types: reward-maximizing habitual behavior, which is fast while inflexible; and goal-directed behavior, which is flexible while slow. Conventionally, habitual and goal-directed behaviors are considered handled by two distinct systems in the brain. Here, we propose to bridge the gap between the two behaviors, drawing on the principles of variational Bayesian theory. We incorporate both behaviors in one framework by introducing a Bayesian latent variable called "intention". The habitual behavior is generated by using prior distribution of intention, which is goal-less; and the goal-directed behavior is generated by the posterior distribution of intention, which is conditioned on the goal. Building on this idea, we present a novel Bayesian framework for modeling behaviors. Our proposed framework enables skill sharing between the two kinds of behaviors, and by leveraging the idea of predictive coding, it enables an agent to seamlessly generalize from habitual to goal-directed behavior without requiring additional training. The proposed framework suggests a fresh perspective for cognitive science and embodied AI, highlighting the potential for greater integration between habitual and goal-directed behaviors.

We consider the problem of Bayesian parameter estimation for deep neural networks, which is important in problem settings where we may have little data, and/ or where we need accurate posterior predictive densities p(y|x, D), e.g., for applications involving bandits or active learning. One simple approach to this is to use online Monte Carlo methods, such as SGLD (stochastic gradient Langevin dynamics). Unfortunately, such a method needs to store many copies of the parameters (which wastes memory), and needs to make predictions using many versions of the model (which wastes time). We describe a method for "distilling" a Monte Carlo approximation to the posterior predictive density into a more compact form, namely a single deep neural network. We compare to two very recent approaches to Bayesian neural networks, namely an approach based on expectation propagation [HLA15] and an approach based on variational Bayes [BCKW15]. Our method performs better than both of these, is much simpler to implement, and uses less computation at test time.

Mean field variational Bayes (MFVB) is a popular posterior approximation method due to its fast runtime on large-scale data sets. However, a well known major failing of MFVB is that it underestimates the uncertainty of model variables (sometimes severely) and provides no information about model variable covariance. We generalize linear response methods from statistical physics to deliver accurate uncertainty estimates for model variables--both for individual variables and coherently across variables. We call our method linear response variational Bayes (LRVB). When the MFVB posterior approximation is in the exponential family, LRVB has a simple, analytic form, even for non-conjugate models. Indeed, we make no assumptions about the form of the true posterior. We demonstrate the accuracy and scalability of our method on a range of models for both simulated and real data.

Variational inference is a scalable technique for approximate Bayesian inference. Deriving variational inference algorithms requires tedious model-specific calculations; this makes it difficult for non-experts to use.

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 ɛ-ball around the observed data, which is only correct in the limit ɛ 0. Monte Carlo methods can then draw samples from the approximate posterior to approximate predictions or error bars on parameters.

Variational inference (VI) seeks to approximate a target distribution $\pi$ by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates $\pi$ by minimizing the Kullback-Leibler (KL) divergence to $\pi$ over the space of Gaussians. In this work, we develop the (Stochastic) Forward-Backward Gaussian Variational Inference (FB-GVI) algorithm to solve Gaussian VI. Our approach exploits the composite structure of the KL divergence, which can be written as the sum of a smooth term (the potential) and a non-smooth term (the entropy) over the Bures-Wasserstein (BW) space of Gaussians endowed with the Wasserstein distance. For our proposed algorithm, we obtain state-of-the-art convergence guarantees when $\pi$ is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when $\pi$ is only log-smooth.

Humans cannot always be treated as oracles for collaborative sensing. Robots thus need to maintain beliefs over unknown world states when receiving semantic data from humans, as well as account for possible discrepancies between human-provided data and these beliefs. To this end, this paper introduces the problem of semantic data association (SDA) in relation to conventional data association problems for sensor fusion. It then develops a novel probabilistic semantic data association (PSDA) algorithm to rigorously address SDA in general settings, unlike previous work on semantic data fusion which developed heuristic techniques for specific settings. PSDA is further incorporated into a recursive hybrid Bayesian data fusion scheme which uses Gaussian mixture priors for object states and softmax functions for semantic human sensor data likelihoods. Simulations of a multi-object search task show that PSDA enables robust collaborative state estimation under a wide range of conditions where semantic human sensor data can be erroneous or contain significant reference ambiguities.