Reinforcement learning from human feedback (RLHF) is a popular technique for training high-quality AI assistants. However, RLHF may also encourage model responses that match user beliefs over truthful responses, a behavior known as sycophancy. We investigate the prevalence of sycophancy in RLHF-trained models and whether human preference judgments are responsible. We first demonstrate that five state-of-the-art AI assistants consistently exhibit sycophancy behavior across four varied free-form text-generation tasks. To understand if human preferences drive this broadly observed behavior of RLHF models, we analyze existing human preference data. We find that when a response matches a user's views, it is more likely to be preferred. Moreover, both humans and preference models (PMs) prefer convincingly-written sycophantic responses over correct ones a non-negligible fraction of the time. Optimizing model outputs against PMs also sometimes sacrifices truthfulness in favor of sycophancy. Overall, our results indicate that sycophancy is a general behavior of RLHF models, likely driven in part by human preference judgments favoring sycophantic responses.

Identifying how much a model $\hat{p}_{Y|X}^{\theta}$ knows about the stochastic real-world process $p_{Y|X}$ it was trained on is important to ensure it avoids producing incorrect or "hallucinated" answers or taking unsafe actions. But this is difficult for generative models because probabilistic predictions do not distinguish between per-response noise (aleatoric uncertainty) and lack of knowledge about the process (epistemic uncertainty), and existing epistemic uncertainty quantification techniques tend to be overconfident when the model underfits. We propose a general strategy for teaching a model to both approximate $p_{Y|X}$ and also estimate the remaining gaps between $\hat{p}_{Y|X}^{\theta}$ and $p_{Y|X}$: train it to predict pairs of independent responses drawn from the true conditional distribution, allow it to "cheat" by observing one response while predicting the other, then measure how much it cheats. Remarkably, we prove that being good at cheating (i.e. cheating whenever it improves your prediction) is equivalent to being second-order calibrated, a principled extension of ordinary calibration that allows us to construct provably-correct frequentist confidence intervals for $p_{Y|X}$ and detect incorrect responses with high probability. We demonstrate empirically that our approach accurately estimates how much models don’t know across ambiguous image classification, (synthetic) language modeling, and partially-observable navigation tasks, outperforming existing techniques.

We investigate a family of simple long-context attacks on large language models: prompting with hundreds of demonstrations of undesirable behavior. This attack is newly feasible with the larger context windows recently deployed by language model providers like Google DeepMind, OpenAI and Anthropic. We find that in diverse, realistic circumstances, the effectiveness of this attack follows a power law, up to hundreds of shots. We demonstrate the success of this attack on the most widely used state-of-the-art closed-weight models, and across various tasks. Our results suggest very long contexts present a rich new attack surface for LLMs.

Machine learning practitioners often face significant challenges in formally integrating their prior knowledge and beliefs into predictive models, limiting the potential for nuanced and context-aware analyses. Moreover, the expertise needed to integrate this prior knowledge into probabilistic modeling typically limits the application of these models to specialists. Our goal is to build a regression model that can process numerical data and make probabilistic predictions at arbitrary locations, guided by natural language text which describes a user's prior knowledge. Large Language Models (LLMs) provide a useful starting point for designing such a tool since they 1) provide an interface where users can incorporate expert insights in natural language and 2) provide an opportunity for leveraging latent problem-relevant knowledge encoded in LLMs that users may not have themselves. We start by exploring strategies for eliciting explicit, coherent numerical predictive distributions from LLMs. We examine these joint predictive distributions, which we call LLM Processes, over arbitrarily-many quantities in settings such as forecasting, multi-dimensional regression, black-box optimization, and image modeling. We investigate the practical details of prompting to elicit coherent predictive distributions, and demonstrate their effectiveness at regression. Finally, we demonstrate the ability to usefully incorporate text into numerical predictions, improving predictive performance and giving quantitative structure that reflects qualitative descriptions. This lets us begin to explore the rich, grounded hypothesis space that LLMs implicitly encode.

It is important that consumers and regulators can verify the provenance of large neural models to evaluate their capabilities and risks. We introduce the concept of a "Proof-of-Training-Data": any protocol that allows a model trainer to convince a Verifier of the training data that produced a set of model weights. Such protocols could verify the amount and kind of data and compute used to train the model, including whether it was trained on specific harmful or beneficial data sources. We explore efficient verification strategies for Proof-of-Training-Data that are compatible with most current large-model training procedures. These include a method for the model-trainer to verifiably pre-commit to a random seed used in training, and a method that exploits models' tendency to temporarily overfit to training data in order to detect whether a given data-point was included in training. We show experimentally that our verification procedures can catch a wide variety of attacks, including all known attacks from the Proof-of-Learning literature.

We generalize gradient descent with momentum for optimization in differentiable games to have complex-valued momentum. We give theoretical motivation for our method by proving convergence on bilinear zero-sum games for simultaneous and alternating updates. Our method gives real-valued parameter updates, making it a drop-in replacement for standard optimizers. We empirically demonstrate that complex-valued momentum can improve convergence in realistic adversarial games–like generative adversarial networks– by showing we can find better solutions with an almost identical computational cost. We also show a practical complex-valued Adam variant, which we use to train BigGAN to improve inception scores on CIFAR-10.

We perform scalable approximate inference in continuous-depth Bayesian neural networks. In this model class, uncertainty about separate weights in each layer gives hidden units that follow a stochastic differential equation. We demonstrate gradient-based stochastic variational inference in this infinite-parameter setting, producing arbitrarily-flexible approximate posteriors. We also derive a novel gradient estimator that approaches zero variance as the approximate posterior over weights approaches the true posterior. This approach brings continuous-depth Bayesian neural nets to a competitive comparison against discrete-depth alternatives, while inheriting the memory-efficient training and tunable precision of Neural ODEs.

Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems involve inner and outer parameters, each optimized for its own objective. Often, at least one of the two levels is underspecified and there are multiple ways to choose among equivalent optima. Inspired by recent studies of the implicit bias induced by optimization algorithms in single-level optimization, we investigate the implicit bias of different gradient-based algorithms for jointly optimizing the inner and outer parameters. We delineate two standard BLO methods—cold-start and warm-start BLO—and show that the converged solution or long-run behavior depends to a large degree on these and other algorithmic choices, such as the hypergradient approximation. We also show that the solutions from warm-start BLO can encode a surprising amount of information about the outer objective, even when the outer optimization variables are low-dimensional. We believe that implicit bias deserves as central a role in the study of bilevel optimization as it has attained in the study of single-level neural net optimization.

We propose a general and scalable approximate sampling strategy for probabilistic models with discrete variables. Our approach uses gradients of the likelihood function with respect to its discrete inputs to propose updates in a Metropolis-Hastings sampler. We show empirically that this approach outperforms generic samplers in a number of difficult settings including Ising models, Potts models, restricted Boltzmann machines, and factorial hidden Markov models. We also demonstrate our improved sampler for training deep energy-based models on high dimensional discrete image data. This approach outperforms variational auto-encoders and existing energy-based models. Finally, we give bounds showing that our approach is near-optimal in the class of samplers which propose local updates.

Pre-training (PT) followed by fine-tuning (FT) is an effective method for training neural networks, and has led to significant performance improvements in many domains. PT can incorporate various design choices such as task and data reweighting strategies, augmentation policies, and noise models, all of which can significantly impact the quality of representations learned. The hyperparameters introduced by these strategies therefore must be tuned appropriately. However, setting the values of these hyperparameters is challenging. Most existing methods either struggle to scale to high dimensions, are too slow and memory-intensive, or cannot be directly applied to the two-stage PT and FT learning process. In this work, we propose an efficient, gradient-based algorithm to meta-learn PT hyperparameters. We formalize the PT hyperparameter optimization problem and propose a novel method to obtain PT hyperparameter gradients by combining implicit differentiation and backpropagation through unrolled optimization. We demonstrate that our method improves predictive performance on two real-world domains. First, we optimize high-dimensional task weighting hyperparameters for multitask pre-training on protein-protein interaction graphs and improve AUROC by up to 3.9%. Second, we optimize a data augmentation neural network for self-supervised PT with SimCLR on electrocardiography data and improve AUROC by up to 1.9%.

We present a novel programming language design that attempts to combine the clarity and safety of high-level functional languages with the efficiency and parallelism of low-level numerical languages. We treat arrays as eagerly-memoized functions on typed index sets, allowing abstract function manipulations, such as currying, to work on arrays. In contrast to composing primitive bulk-array operations, we argue for an explicit nested indexing style that mirrors application of functions to arguments. We also introduce a fine-grained typed effects system which affords concise and automatically-parallelized in-place updates. Specifically, an associative accumulation effect allows reverse-mode automatic differentiation of in-place updates in a way that preserves parallelism. Empirically, we benchmark against the Futhark array programming language, and demonstrate that aggressive inlining and type-driven compilation allows array programs to be written in an expressive, "pointful" style with little performance penalty.

The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. Specifically, we derive a stochastic differentialequation whose solution is the gradient, a memory-efficient algorithm for cachingnoise, and conditions under which numerical solutions converge. In addition, we combine our method with gradient-based stochastic variational inference for latent stochastic differential equations. We use our method to fit stochastic dynamics defined by neural networks, achieving competitive performance ona 50-dimensional motion capture dataset.

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network—where every weight is a hyperparameter tuned for validation performance—outputting augmented training examples. Jointly tuning weights and hyper-parameters is only a few times more costly in memory and compute than standard training.

We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model’s log-density. We estimate the Stein discrepancy between the data density p(x) and the model density q(x) based on a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize this discrepancy. This yields a novel goodness-of-fit test which outperforms existing methods on high dimensional data. Furthermore, optimizing q(x) to minimize this discrepancy produces a novel method for training unnormalized models. This training method can fit large unnormalized models faster than existing approaches. The ability to both learn and compare models is a unique feature of the proposed method.

Differential equations parameterized by neural networks become expensive to solve numerically as training progresses. We propose a remedy that encourages learned dynamics to be easier to solve. Specifically, we introduce a differentiable surrogate for the time cost of standard numerical solvers, using higher-order derivatives of solution trajectories. These derivatives are efficient to compute with Taylor-mode automatic differentiation. Optimizing this additional objective trades model performance against the time cost of solving the learned dynamics. We demonstrate our approach by training substantially faster, while nearly as accurate, models in supervised classification, density estimation, and time-series modelling tasks.

Explanations of time series models are useful for high stakes applications like healthcare but have received little attention in machine learning literature. We propose FIT, a framework that evaluates the importance of observations for a multivariate time-series black-box model by quantifying the shift in the predictive distribution over time. FIT defines the importance of an observation based on its contribution to the distributional shift under a KL-divergence that contrasts the predictive distribution against a counterfactual where the rest of the features are unobserved. We also demonstrate the need to control for time-dependent distribution shifts. We compare with state-of-the-art baselines on simulated and real-world clinical data and demonstrate that our approach is superior in identifying important time points and observations throughout the time series.

Word embeddings are often criticized for capturing undesirable word associations such as gender stereotypes.However, methods for measuring and removing such biases remain poorly understood.We show that for any embedding model that implicitly does matrix factorization, debiasing vectors post hoc using subspace projection (Bolukbasi et al., 2016) is, under certain conditions, equivalent to training on an unbiased corpus.We also prove that WEAT, the most common association test for word embeddings, systematically overestimates bias.Given that the subspace projection method is provably effective, we use it to derive a new measure of association called the relational inner product association (RIPA).Experiments with RIPA reveal that, on average, skipgram with negative sampling (SGNS) does not make most words any more gendered than they are in the training corpus.However, for gender-stereotyped words, SGNS actually amplifies the gender association in the corpus.

A surprising property of word vectors is that word analogies can often be solved with vector arithmetic.However, it is unclear why arithmetic operators correspond to non-linear embedding models such as skip-gram with negative sampling (SGNS).We provide a formal explanation of this phenomenon without making the strong assumptions that past theories have made about the vector space and word distribution.Our theory has several implications.Past work has conjectured that linear substructures exist in vector spaces because relations can be represented as ratios; we prove that this holds for SGNS.We provide novel justification for the addition of SGNS word vectors by showing that it automatically downweights the more frequent word, as weighting schemes do ad hoc.Lastly, we offer an information theoretic interpretation of Euclidean distance in vector spaces, justifying its use in capturing word dissimilarity.

We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting network architectures. In contrast, our approach only requires adding a simple normalization step during training, already available in standard frameworks. Invertible ResNets define a generative model which can be trained by maximum likelihood on unlabeled data. To compute likelihoods, we introduce a tractable approximation to the Jacobian log-determinant of a residual block. Our empirical evaluation shows that invertible ResNets perform competitively with both state-of-the-art image classifiers and flow-based generative models, something that has not been previously achieved with a single architecture.

Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforcing invertibility. However, prior work trained invertible residual networks for density estimation by relying on biased log-density estimates whose bias increased with the network's expressiveness. We give a tractable unbiased estimate of the log density, and reduce the memory required during training by a factor of ten. Furthermore, we improve invertible residual blocks by proposing the use of activation functions that avoid gradient saturation and generalizing the Lipschitz condition to induced mixed norms. The resulting approach, called Residual Flows, achieves state-of-the-art performance on density estimation amongst flow-based models, and outperforms networks that use coupling blocks at joint generative and discriminative modeling.

Gradients of neural networks can be computed efficiently for any architecture, but some applications require computing differential operators with higher time complexity. We describe a family of neural network architectures that allow easy access to a family of differential operators involving \emph{dimension-wise derivatives}, and we show how to modify the backward computation graph to compute them efficiently. We demonstrate the use of these operators for solving root-finding subproblems in implicit ODE solvers, exact density evaluation for continuous normalizing flows, and evaluating the Fokker-Planck equation for training stochastic differential equation models.

We propose a new family of efficient and expressive deep generative models of graphs, called Graph Recurrent Attention Networks (GRANs). Our model generates graphs one block of nodes and associated edges at a time. The block size and sampling stride allow us to trade off sample quality for efficiency. Compared to previous RNN-based graph generative models, our framework better captures the auto-regressive conditioning between the already-generated and to-be-generated parts of the graph using Graph Neural Networks (GNNs) with attention. This not only reduces the dependency on node ordering but also bypasses the long-term bottleneck caused by the sequential nature of RNNs. Moreover, we parameterize the output distribution per block using a mixture of Bernoulli, which captures the correlations among generated edges within the block. Finally, we propose to handle node orderings in generation by marginalizing over a family of canonical orderings. On standard benchmarks, we achieve state-of-the-art time efficiency and sample quality compared to previous models. Additionally, we show our model is capable of generating large graphs of up to 5K nodes with good quality. Our code is released at: \url{https://github.com/lrjconan/GRAN}.

Time series with non-uniform intervals occur in many applications, and are difficult to model using standard recurrent neural networks (RNNs). We generalize RNNs to have continuous-time hidden dynamics defined by ordinary differential equations (ODEs), a model we call ODE-RNNs. Furthermore, we use ODE-RNNs to replace the recognition network of the recently-proposed Latent ODE model. Both ODE-RNNs and Latent ODEs can naturally handle arbitrary time gaps between observations, and can explicitly model the probability of observation times using Poisson processes. We show experimentally that these ODE-based models outperform their RNN-based counterparts on irregularly-sampled data.

Abstract We propose the first reduced model simulation framework for deformable solid dynamics using autoencoder neural networks. We provide a data‐driven approach to generating nonlinear reduced spaces for deformation dynamics. In contrast to previous methods using machine learning which accelerate simulation by approximating the time‐stepping function, we solve the true equations of motion in the latent‐space using a variational formulation of implicit integration. Our approach produces drastically smaller reduced spaces than conventional linear model reduction, improving performance and robustness. Furthermore, our method works well with existing force‐approximation cubature methods.

Amortized inference allows latent-variable models trained via variational learning to scale to large datasets. The quality of approximate inference is determined by two factors: a) the capacity of the variational distribution to match the true posterior and b) the ability of the recognition network to produce good variational parameters for each datapoint. We examine approximate inference in variational autoencoders in terms of these factors. We find that divergence from the true posterior is often due to imperfect recognition networks, rather than the limited complexity of the approximating distribution. We show that this is due partly to the generator learning to accommodate the choice of approximation. Furthermore, we show that the parameters used to increase the expressiveness of the approximation play a role in generalizing inference rather than simply improving the complexity of the approximation.

Variational Bayesian neural nets combine the flexibility of deep learning with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff between cheap but simple variational families (e.g. fully factorized) or expensive and complicated inference procedures. We show that natural gradient ascent with adaptive weight noise implicitly fits a variational posterior to maximize the evidence lower bound (ELBO). This insight allows us to train full-covariance, fully factorized, or matrix-variate Gaussian variational posteriors using noisy versions of natural gradient, Adam, and K-FAC, respectively, making it possible to scale up to modern-size ConvNets. On standard regression benchmarks, our noisy K-FAC algorithm makes better predictions and matches Hamiltonian Monte Carlo’s predictive variances better than existing methods. Its improved uncertainty estimates lead to more efficient exploration in active learning, and intrinsic motivation for reinforcement learning.

We decompose the evidence lower bound to show the existence of a term measuring the total correlation between latent variables. We use this to motivate the beta-TCVAE (Total Correlation Variational Autoencoder) algorithm, a refinement and plug-in replacement of the beta-VAE for learning disentangled representations, requiring no additional hyperparameters during training. We further propose a principled classifier-free measure of disentanglement called the mutual information gap (MIG). We perform extensive quantitative and qualitative experiments, in both restricted and non-restricted settings, and show a strong relation between total correlation and disentanglement, when the model is trained using our framework.

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a blackbox differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.

We propose a simple and general variant of the standard reparameterized gradient estimator for the variational evidence lower bound. Specifically, we remove a part of the total derivative with respect to the variational parameters that corresponds to the score function. Removing this term produces an unbiased gradient estimator whose variance approaches zero as the approximate posterior approaches the exact posterior. We analyze the behavior of this gradient estimator theoretically and empirically, and generalize it to more complex variational distributions such as mixtures and importance-weighted posteriors.

We show that unconverged stochastic gradient descent can be interpreted as sampling from a nonparametric approximate posterior distribution. This distribution is implicitly defined by the transformation of an initial distribution by a sequence of optimization steps. By tracking the change in entropy of this distribution during optimization, we give a scalable, unbiased estimate of a variational lower bound on the log marginal likelihood. This bound can be used to optimize hyperparameters instead of cross-validation. This Bayesian interpretation of SGD also suggests new overfitting-resistant optimization procedures, and gives a theoretical foundation for early stopping and ensembling. We investigate the properties of this marginal likelihood estimator on neural network models.

Novice composers often find it difficult to go beyond common chord progressions. To make it easier for composers to experiment with radical chord choices, we built a creativity support tool, ChordRipple, which makes chord recommendations that aim to be both diverse and appropriate to the current context. Composers can use it to help select the next chord, or to replace sequences of chords in an internally consistent manner. To make such recommendations, we adapt a neural network model from natural language processing known as Word2Vec to the music domain. This model learns chord embeddings from a corpus of chord sequences, placing chords nearby when they are used in similar contexts. The learned embeddings support creative substitutions between chords, and also exhibit topological properties that correspond to musical structure. For example, the major and minor chords are both arranged in the latent space in shapes corresponding to the circle-of-fifths. Our structured observations with 14 music students show that the tool helped them explore a wider palette of chords, and to make "big jumps in just a few chords". It gave them "new ideas of ways to move forward in the piece", not just on a chord-to-chord level but also between phrases. Our controlled studies with 9 more music students show that more adventurous chords are adopted when composing with ChordRipple.

We propose a general modeling and inference framework that combines the complementary strengths of probabilistic graphical models and deep learning methods. Our model family composes latent graphical models with neural network observation likelihoods. For inference, we use recognition networks to produce local evidence potentials, then combine them with the model distribution using efficient message-passing algorithms. All components are trained simultaneously with a single stochastic variational inference objective. We illustrate this framework by automatically segmenting and categorizing mouse behavior from raw depth video, and demonstrate several other example models.

How do people learn about complex functional structure? Taking inspiration from other areas of cognitive science, we propose that this is accomplished by harnessing compositionality: complex structure is decomposed into simpler building blocks. We formalize this idea within the framework of Bayesian regression using a grammar over Gaussian process kernels. We show that participants prefer compositional over non-compositional function extrapolations, that samples from the human prior over functions are best described by a compositional model, and that people perceive compositional functions as more predictable than their non-compositional but otherwise similar counterparts. We argue that the compositional nature of intuitive functions is consistent with broad principles of human cognition.

Tuning hyperparameters of learning algorithms is hard because gradients are usually unavailable. We compute exact gradients of cross-validation performance with respect to all hyperparameters by chaining derivatives backwards through the entire training procedure. These gradients allow us to optimize thousands of hyperparameters, including step-size and momentum schedules, weight initialization distributions, richly parameterized regularization schemes, and neural network architectures. We compute hyperparameter gradients by exactly reversing the dynamics of stochastic gradient descent with momentum.

We introduce a convolutional neural network that operates directly on graphs.These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape.The architecture we present generalizes standard molecular feature extraction methods based on circular fingerprints.We show that these data-driven features are more interpretable, and have better predictive performance on a variety of tasks.

This paper presents the beginnings of an automatic statistician, focusing on regression problems. Our system explores an open-ended space of statistical models to discover a good explanation of a data set, and then produces a detailed report with figures and natural-language text. Our approach treats unknown regression functions nonparametrically using Gaussian processes, which has two important consequences. First, Gaussian processes can model functions in terms of high-level properties (e.g. smoothness, trends, periodicity, changepoints). Taken together with the compositional structure of our language of models this allows us to automatically describe functions in simple terms. Second, the use of flexible nonparametric models and a rich language for composing them in an open-ended manner also results in state-of-the-art extrapolation performance evaluated over 13 real time series data sets from various domains.

Choosing appropriate architectures and regularization strategies of deep networks is crucial to good predictive performance. To shed light on this problem, we analyze the analogous problem of constructing useful priors on compositions of functions. Specifically, we study the deep Gaussian process, a type of infinitely-wide, deep neural network. We show that in standard architectures, the representational capacity of the network tends to capture fewer degrees of freedom as the number of layers increases, retaining only a single degree of freedom in the limit. We propose an alternate network architecture which does not suffer from this pathology. We also examine deep covariance functions, obtained by composing infinitely many feature transforms. Lastly, we characterize the class of models obtained by performing dropout on Gaussian processes.

Typical synthesizers only provide controls to the low-level parameters of sound-synthesis, such as wave-shapes or filter envelopes. In contrast, composers often want to adjust and express higher-level qualities, such as how "scary" or "steady" sounds are perceived to be. We develop a system which allows users to directly control abstract, high-level qualities of sounds. To do this, our system learns functions that map from synthesizer control settings to perceived levels of high-level qualities. Given these functions, our system can generate high-level knobs that directly adjust sounds to have more or less of those qualities. We model the functions mapping from control-parameters to the degree of each high-level quality using Gaussian processes, a nonparametric Bayesian model. These models can adjust to the complexity of the function being learned, account for nonlinear interaction between control-parameters, and allow us to characterize the uncertainty about the functions being learned. By tracking uncertainty about the functions being learned, we can use active learning to quickly calibrate the tool, by querying the user about the sounds the system expects to most improve its performance. We show through simulations that this model-based active learning approach learns high-level knobs on certain classes of target concepts faster than several baselines, and give examples of the resulting automatically- constructed knobs which adjust levels of non-linear, high- level concepts.

Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base kernels. We present a method for searching over this space of structures which mirrors the scientific discovery process. The learned structures can often decompose functions into interpretable components and enable long-range extrapolation on time-series datasets. Our structure search method outperforms many widely used kernels and kernel combination methods on a variety of prediction tasks.

Numerical integration is an key component of many problems in scientific computing, statistical modelling, and machine learning. Bayesian Quadrature is a model-based method for numerical integration which, relative to standard Monte Carlo methods, offers increased sample efficiency and a more robust estimate of the uncertainty in the estimated integral. We propose a novel Bayesian Quadrature approach for numerical integration when the integrand is non-negative, such as the case of computing the marginal likelihood, predictive distribution, or normalising constant of a probabilistic model. Our approach approximately marginalises the quadrature model's hyperparameters in closed form, and introduces an active learning scheme to optimally select function evaluations, as opposed to using Monte Carlo samples. We demonstrate our method on both a number of synthetic benchmarks and a real scientific problem from astronomy.

We introduce a Gaussian process model of functions which are additive. An additive function is one which decomposes into a sum of low-dimensional functions, each depending on only a subset of the input variables. Additive GPs generalize both Generalized Additive Models, and the standard GP models which use squared-exponential kernels. Hyperparameter learning in this model can be seen as Bayesian Hierarchical Kernel Learning (HKL). We introduce an expressive but tractable parameterization of the kernel function, which allows efficient evaluation of all input interaction terms, whose number is exponential in the input dimension. The additional structure discoverable by this model results in increased interpretability, as well as state-of-the-art predictive power in regression tasks.