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We show how rational function approximations to the logarithm, such as $\log z \approx (z^2 - 1)/(z^2 + 6z + 1)$, can be turned into fast algorithms for approximating the determinant of a very large matrix. We empirically demonstrate that when combined with a good preconditioner, the third order rational function approximation offers a very good trade-off between speed and accuracy when measured on matrices coming from Mat\'ern-$5/2$ and radial basis function Gaussian process kernels. In particular, it is significantly more accurate on those matrices than the state-of-the-art stochastic Lanczos quadrature method for approximating determinants while running at about the same speed., Comment: 22 pages, 17 figures

Spatiotemporal datasets, which consist of spatially-referenced time series, are ubiquitous in many scientific and business-intelligence applications, such as air pollution monitoring, disease tracking, and cloud-demand forecasting. As modern datasets continue to increase in size and complexity, there is a growing need for new statistical methods that are flexible enough to capture complex spatiotemporal dynamics and scalable enough to handle large prediction problems. This work presents the Bayesian Neural Field (BayesNF), a domain-general statistical model for inferring rich probability distributions over a spatiotemporal domain, which can be used for data-analysis tasks including forecasting, interpolation, and variography. BayesNF integrates a novel deep neural network architecture for high-capacity function estimation with hierarchical Bayesian inference for robust uncertainty quantification. By defining the prior through a sequence of smooth differentiable transforms, posterior inference is conducted on large-scale data using variationally learned surrogates trained via stochastic gradient descent. We evaluate BayesNF against prominent statistical and machine-learning baselines, showing considerable improvements on diverse prediction problems from climate and public health datasets that contain tens to hundreds of thousands of measurements. The paper is accompanied with an open-source software package (https://github.com/google/bayesnf) that is easy-to-use and compatible with modern GPU and TPU accelerators on the JAX machine learning platform., Comment: 27 pages, 7 figures, 3 tables, 2 listings

How do we infer a 3D scene from a single image in the presence of corruptions like rain, snow or fog? Straightforward domain randomization relies on knowing the family of corruptions ahead of time. Here, we propose a Bayesian approach-dubbed robust inverse graphics (RIG)-that relies on a strong scene prior and an uninformative uniform corruption prior, making it applicable to a wide range of corruptions. Given a single image, RIG performs posterior inference jointly over the scene and the corruption. We demonstrate this idea by training a neural radiance field (NeRF) scene prior and using a secondary NeRF to represent the corruptions over which we place an uninformative prior. RIG, trained only on clean data, outperforms depth estimators and alternative NeRF approaches that perform point estimation instead of full inference. The results hold for a number of scene prior architectures based on normalizing flows and diffusion models. For the latter, we develop reconstruction-guidance with auxiliary latents (ReGAL)-a diffusion conditioning algorithm that is applicable in the presence of auxiliary latent variables such as the corruption. RIG demonstrates how scene priors can be used beyond generation tasks., Comment: ICML submission. Reworked main body, new appendix figures

Robots cannot yet match humans' ability to rapidly learn the shapes of novel 3D objects and recognize them robustly despite clutter and occlusion. We present Bayes3D, an uncertainty-aware perception system for structured 3D scenes, that reports accurate posterior uncertainty over 3D object shape, pose, and scene composition in the presence of clutter and occlusion. Bayes3D delivers these capabilities via a novel hierarchical Bayesian model for 3D scenes and a GPU-accelerated coarse-to-fine sequential Monte Carlo algorithm. Quantitative experiments show that Bayes3D can learn 3D models of novel objects from just a handful of views, recognizing them more robustly and with orders of magnitude less training data than neural baselines, and tracking 3D objects faster than real time on a single GPU. We also demonstrate that Bayes3D learns complex 3D object models and accurately infers 3D scene composition when used on a Panda robot in a tabletop scenario.

This paper presents a new approach to automatically discovering accurate models of complex time series data. Working within a Bayesian nonparametric prior over a symbolic space of Gaussian process time series models, we present a novel structure learning algorithm that integrates sequential Monte Carlo (SMC) and involutive MCMC for highly effective posterior inference. Our method can be used both in "online" settings, where new data is incorporated sequentially in time, and in "offline" settings, by using nested subsets of historical data to anneal the posterior. Empirical measurements on real-world time series show that our method can deliver 10x--100x runtime speedups over previous MCMC and greedy-search structure learning algorithms targeting the same model family. We use our method to perform the first large-scale evaluation of Gaussian process time series structure learning on a prominent benchmark of 1,428 econometric datasets. The results show that our method discovers sensible models that deliver more accurate point forecasts and interval forecasts over multiple horizons as compared to widely used statistical and neural baselines that struggle on this challenging data., Comment: 17 pages, 8 figures, 2 tables. Appearing in ICML 2023

Multichannel, infinite-conjugate optical systems easily allow implementation of multiple image paths and imaging modes into a single microscope. Traditional optical alignment methods which rely on additional hardware are not always simple to implement, particularly in compact open-source microscope designs. We present here an alignment algorithm and process to position the lenses and cameras in a microscope using only image magnification measurements. We show that the resulting positioning accuracy is comparable to the axial resolution of the microscope. Ray transfer matrix analysis is used to model the imaging paths when the optics are both correctly and incorrectly aligned. This is used to derive the corresponding image magnifications. We can then extract information about the lens positions using simple image-based measurements to determine whether there is misalignment of the objective lens to sample distance (working distance) and with what magnitude and direction the objective lens needs to be adjusted. Using the M4All open-source 3D printable microscope system in combination with the OpenFlexure microscope, we validate the alignment method and highlight its usability. We provide the model and an example implementation of the algorithm as an open-source Jupyter Notebook.

We present a general approach to batching arbitrary computations for accelerators such as GPUs. We show orders-of-magnitude speedups using our method on the No U-Turn Sampler (NUTS), a workhorse algorithm in Bayesian statistics. The central challenge of batching NUTS and other Markov chain Monte Carlo algorithms is data-dependent control flow and recursion. We overcome this by mechanically transforming a single-example implementation into a form that explicitly tracks the current program point for each batch member, and only steps forward those in the same place. We present two different batching algorithms: a simpler, previously published one that inherits recursion from the host Python, and a more complex, novel one that implemenents recursion directly and can batch across it. We implement these batching methods as a general program transformation on Python source. Both the batching system and the NUTS implementation presented here are available as part of the popular TensorFlow Probability software package., Comment: 10 pages; Machine Learning and Systems 2020

Recent deep learning approaches have achieved impressive performance on speech enhancement and separation tasks. However, these approaches have not been investigated for separating mixtures of arbitrary sounds of different types, a task we refer to as universal sound separation, and it is unknown how performance on speech tasks carries over to non-speech tasks. To study this question, we develop a dataset of mixtures containing arbitrary sounds, and use it to investigate the space of mask-based separation architectures, varying both the overall network architecture and the framewise analysis-synthesis basis for signal transformations. These network architectures include convolutional long short-term memory networks and time-dilated convolution stacks inspired by the recent success of time-domain enhancement networks like ConvTasNet. For the latter architecture, we also propose novel modifications that further improve separation performance. In terms of the framewise analysis-synthesis basis, we explore both a short-time Fourier transform (STFT) and a learnable basis, as used in ConvTasNet. For both of these bases, we also examine the effect of window size. In particular, for STFTs, we find that longer windows (25-50 ms) work best for speech/non-speech separation, while shorter windows (2.5 ms) work best for arbitrary sounds. For learnable bases, shorter windows (2.5 ms) work best on all tasks. Surprisingly, for universal sound separation, STFTs outperform learnable bases. Our best methods produce an improvement in scale-invariant signal-to-distortion ratio of over 13 dB for speech/non-speech separation and close to 10 dB for universal sound separation., Comment: 5 pages, accepted to WASPAA 2019

In recent years, deep networks have led to dramatic improvements in speech enhancement by framing it as a data-driven pattern recognition problem. In many modern enhancement systems, large amounts of data are used to train a deep network to estimate masks for complex-valued short-time Fourier transforms (STFTs) to suppress noise and preserve speech. However, current masking approaches often neglect two important constraints: STFT consistency and mixture consistency. Without STFT consistency, the system's output is not necessarily the STFT of a time-domain signal, and without mixture consistency, the sum of the estimated sources does not necessarily equal the input mixture. Furthermore, the only previous approaches that apply mixture consistency use real-valued masks; mixture consistency has been ignored for complex-valued masks. In this paper, we show that STFT consistency and mixture consistency can be jointly imposed by adding simple differentiable projection layers to the enhancement network. These layers are compatible with real or complex-valued masks. Using both of these constraints with complex-valued masks provides a 0.7 dB increase in scale-invariant signal-to-distortion ratio (SI-SDR) on a large dataset of speech corrupted by a wide variety of nonstationary noise across a range of input SNRs.

We explore a variety of neural networks configurations for one- and two-channel spectrogram-mask-based speech enhancement. Our best model improves on previous state-of-the-art performance on the CHiME2 speech enhancement task by 0.4 decibels in signal-to-distortion ratio (SDR). We examine trade-offs such as non-causal look-ahead, computation, and parameter count versus enhancement performance and find that zero-look-ahead models can achieve, on average, within 0.03 dB SDR of our best bidirectional model. Further, we find that 200 milliseconds of look-ahead is sufficient to achieve equivalent performance to our best bidirectional model.

Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be investigated via the spectrum of the Hessian of the empirical loss function. Network data can be understood via the eigenstructure of a graph Laplacian matrix using spectral graph theory. Quantum simulations and other many-body problems are often characterized via the eigenvalues of the solution space, as are various dynamic systems. However, naive eigenvalue estimation is computationally expensive even when the matrix can be represented; in many of these situations the matrix is so large as to only be available implicitly via products with vectors. Even worse, one may only have noisy estimates of such matrix vector products. In this work, we combine several different techniques for randomized estimation and show that it is possible to construct unbiased estimators to answer a broad class of questions about the spectra of such implicit matrices, even in the presence of noise. We validate these methods on large-scale problems in which graph theory and random matrix theory provide ground truth.

The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable modular construction of high dimensional distributions and transformations not possible with previous libraries (e.g., pixelCNNs, autoregressive flows, and reversible residual networks). They are the workhorse behind deep probabilistic programming systems like Edward and empower fast black-box inference in probabilistic models built on deep-network components. TensorFlow Distributions has proven an important part of the TensorFlow toolkit within Google and in the broader deep learning community.

Developers of text-to-speech synthesizers (TTS) often make use of human raters to assess the quality of synthesized speech. We demonstrate that we can model human raters' mean opinion scores (MOS) of synthesized speech using a deep recurrent neural network whose inputs consist solely of a raw waveform. Our best models provide utterance-level estimates of MOS only moderately inferior to sampled human ratings, as shown by Pearson and Spearman correlations. When multiple utterances are scored and averaged, a scenario common in synthesizer quality assessment, AutoMOS achieves correlations approaching those of human raters. The AutoMOS model has a number of applications, such as the ability to explore the parameter space of a speech synthesizer without requiring a human-in-the-loop., Comment: 4 pages, 2 figures, 2 tables, NIPS 2016 End-to-end Learning for Speech and Audio Processing Workshop

Light shifts are an important source of noise and systematics in optically pumped magnetometers. We demonstrate that the long spin coherence time in paraffin-coated cells leads to spatial averaging of the light shifts over the entire cell volume. This renders the averaged light shift independent, under certain approximations, of the light-intensity distribution within the sensor cell. These results and the underlying mechanism can be extended to other spatially varying phenomena in anti-relaxation-coated cells with long coherence times., Comment: 6 pages, 4 figures

We demonstrate an all-optical $^{133}$Cs scalar magnetometer, operating in nonzero magnetic field,in which the magnetic resonance is driven by an effective oscillating magnetic field provided by the AC Stark shift of an intensity-modulated laser beam. We achieve a projected shot-noise-limited sensitivity of 1.7 fT/Hz$^{1/2}$ and measure a technical noise floor of 40 fT/Hz$^{1/2}$. These results are essentially identical to a coil-driven scalar magnetometer using the same setup. This all-optical scheme offers advantages over traditional coil-driven magnetometers for use in arrays and in magnetically sensitive fundamental physics experiments e.g., searches for a permanent electric dipole moment of the neutron., Comment: Dedicated to Professor William Happer on the occasion of his 75th birthday

The nonlinear processes responsible for frequency up- and down-conversion of resonant low-intensity laser radiation in Rb vapour have been evaluated from the spatial and temporal properties of blue and mid-IR light resulting from wave mixing., Comment: Presentation at International Conference on Coherent and Nonlinear Optics (ICONO), Moscow, June 2013

We report observation of long-lived spin-singlet states in a 13C-1H spin pair at zero magnetic field. In 13C-labeled formic acid, we observe spin-singlet lifetimes as long as 37 seconds, about a factor of three longer than the T1 lifetime of dipole polarization in the triplet state. We also observe that the lifetime of the singlet-triplet coherence, T2, is longer than T1. Moreover, we demonstrate that this singlet states formed by spins of a heteronucleus and a 1H nucleus, can exhibit longer lifetimes than the respective triplet states in systems consisting of more than two nuclear spins. Although long-lived homonuclear spin-singlet states have been extensively studied, this is the first experimental observation of analogous spin-singlets consisting of a heteronucleus and a proton., Comment: 5 pages, 4 figures

Atomic magnetometry was performed at Earth's magnetic field over a free-space distance of ten meters. Two laser beams aimed at a distant alkali-vapor cell excited and detected the $^{87}$Rb magnetic resonance, allowing the magnetic field within the cell to be interrogated remotely. Operated as a driven oscillator, the magnetometer measured the geomagnetic field with \lessgtrsim{\lesssim}3.5\,pT precision in a $\sim$2\,s data acquisition; this precision was likely limited by ambient field fluctuations. The sensor was also operated in self-oscillating mode with a 5.3\,pT/$\sqrt{\textrm{Hz}}$ noise floor. Further optimization will yield a high-bandwidth, fully remote magnetometer with sub-pT sensitivity., Comment: Accepted to Appl. Phys. Lett.; 3 pages, 3 figures

Stress and strain are important factors in determining the mechanical, electronic, and optical properties of materials, relating to each other by the material's elasticity or stiffness. Both are represented by second rank field tensors with, in general, six independent components. Measurements of these quantities are usually achieved by measuring a property that depends on the translational symmetry and periodicity of the crystal lattice, such as optical phonon energies using Raman spectroscopy, the electronic band gap using cathodoluminescence, photoelasticity via the optical birefringence, or Electron Back Scattering Diffraction (EBSD). A reciprocal relationship therefore exists between the maximum sensitivity of the measurements and the spatial resolution. Furthermore, of these techniques, only EBSD and off-axis Raman spectroscopy allow measurement of all six components of the stress tensor, but neither is able to provide full 3D maps. Here we demonstrate a method for measuring the full stress tensor in diamond, using the spectral and optical polarization properties of the photoluminescence from individual nitrogen vacancy (NV) colour centres. We demonstrate a sensitivity of order 10 MPa, limited by local fluctuations in the stress in the sample, and corresponding to a strain of about 10^-5, comparable with the best sensitivity provided by other techniques. By using the colour centres as built-in local sensors, the technique overcomes the reciprocal relationship between spatial resolution and sensitivity and offers the potential for measuring strains as small as 10^-9 at spatial resolution of order 10 nm. Furthermore it provides a straightforward route to volumetric stress mapping. Aside from its value in understanding strain distributions in diamond, this new approach to stress and strain measurement could be adapted for use in micro or nanoscale sensors., Comment: 12 pages, 5 figures - supplementary informations included in appendix

We report what we believe is the first experimental limit placed on plant biomagnetism. Measurements with a sensitive atomic magnetometer were performed on the Titan arum (Amorphophallus titanum) inflorescence, known for its fast bio-chemical processes while blooming. We find that the surface magnetic field from these processes, projected along the Earth's magnetic field, and measured at the surface of the plant, is less then ~0.6uG., Comment: 5 pages, 5 figures, to be published - modified one sentence in abstract + reformatted fig

A self-oscillating magnetometer based on nonlinear magneto-optical rotation using amplitude-modulated pump light and unmodulated probe light (AM-NMOR) in 87Rb has been constructed and tested towards a goal of airborne detection of magnetic anomalies. In AM-NMOR, stroboscopic optical pumping via amplitude modulation of the pump beam creates alignment of the ground electronic state of the rubidium atoms. The Larmor precession causes an ac rotation of the polarization of a separate probe beam; the polarization rotation frequency provides a measure of the magnetic field. An anti-relaxation coating on the walls of the atomic vapor cell results in a long lifetime of 56 ms for the alignment, which enables precise measurement of the precession frequency. Light is delivered to the magnetometer by polarization-maintaining optical fibers. Tests of the sensitivity include directly measuring the beat frequency between the magnetometer and a commercial instrument and measurements of Earth's field under magnetically quiet conditions, indicating a sensitivity of at least 5 pT/\sqrt{Hz}. Rotating the sensor indicates a heading error of less than 1 nT, limited in part by residual magnetism of the sensor., Comment: 9 pages, 8 figures, submitted to the Proceedings of SPIE

The third-order polarization emitted from groups of individual localized excitonic transitions after pulsed optical excitation is measured. We observe the evolution of the nonlinear response from the case of a free polarization decay for a single transition, to that of a photon echo for many transitions. The echo is shown to arise from the mutual rephasing of the emission from individual transitions.