Stochastic generative models enable us to capture the geometric structure of a data manifold lying in a high dimensional space through a Riemannian metric in the latent space. However, its practical use is rather limited mainly due to inevitable complexity. In this work we propose a surrogate conformal Riemannian metric in the latent space of a generative model that is simple, efficient and robust. This metric is based on a learnable prior that we propose to learn using a basic energy-based model. We theoretically analyze the behavior of the proposed metric and show that it is sensible to use in practice. We demonstrate experimentally the efficiency and robustness, as well as the behavior of the new approximate metric. Also, we show the applicability of the proposed methodology for data analysis in the life sciences.

Nystr\"om approximation is a fast randomized method that rapidly solves kernel ridge regression (KRR) problems through sub-sampling the n-by-n empirical kernel matrix appearing in the objective function. However, the performance of such a sub-sampling method heavily relies on correctly estimating the statistical leverage scores for forming the sampling distribution, which can be as costly as solving the original KRR. In this work, we propose a linear time (modulo poly-log terms) algorithm to accurately approximate the statistical leverage scores in the stationary-kernel-based KRR with theoretical guarantees. Particularly, by analyzing the first-order condition of the KRR objective, we derive an analytic formula, which depends on both the input distribution and the spectral density of stationary kernels, for capturing the non-uniformity of the statistical leverage scores. Numerical experiments demonstrate that with the same prediction accuracy our method is orders of magnitude more efficient than existing methods in selecting the representative sub-samples in the Nystr\"om approximation.

High capacity end-to-end approaches for human motion prediction have the ability to represent subtle nuances in human behavior, but struggle with robustness to out of distribution inputs and tail events. Planning-based prediction, on the other hand, can reliably output decent-but-not-great predictions: it is much more stable in the face of distribution shift, but it has high inductive bias, missing important aspects that drive human decisions, and ignoring cognitive biases that make human behavior suboptimal. In this work, we analyze one family of approaches that strive to get the best of both worlds: use the end-to-end predictor on common cases, but do not rely on it for tail events / out-of-distribution inputs -- switch to the planning-based predictor there. We contribute an analysis of different approaches for detecting when to make this switch, using an autonomous driving domain. We find that promising approaches based on ensembling or generative modeling of the training distribution might not be reliable, but that there very simple methods which can perform surprisingly well -- including training a classifier to pick up on tell-tale issues in predicted trajectories.

Training machine learning (ML) models typically involves expensive iterative optimization. Once the model's final parameters are released, there is currently no mechanism for the entity which trained the model to prove that these parameters were indeed the result of this optimization procedure. Such a mechanism would support security of ML applications in several ways. For instance, it would simplify ownership resolution when multiple parties contest ownership of a specific model. It would also facilitate the distributed training across untrusted workers where Byzantine workers might otherwise mount a denial-of-service by returning incorrect model updates. In this paper, we remediate this problem by introducing the concept of proof-of-learning in ML. Inspired by research on both proof-of-work and verified computations, we observe how a seminal training algorithm, stochastic gradient descent, accumulates secret information due to its stochasticity. This produces a natural construction for a proof-of-learning which demonstrates that a party has expended the compute require to obtain a set of model parameters correctly. In particular, our analyses and experiments show that an adversary seeking to illegitimately manufacture a proof-of-learning needs to perform *at least* as much work than is needed for gradient descent itself. We also instantiate a concrete proof-of-learning mechanism in both of the scenarios described above. In model ownership resolution, it protects the intellectual property of models released publicly. In distributed training, it preserves availability of the training procedure. Our empirical evaluation validates that our proof-of-learning mechanism is robust to variance induced by the hardware (ML accelerators) and software stacks.

Many healthcare decisions involve navigating through a multitude of treatment options in a sequential and iterative manner to find an optimal treatment pathway with the goal of an optimal patient outcome. Such optimization problems may be amenable to reinforcement learning. A reinforcement learning agent could be trained to provide treatment recommendations for physicians, acting as a decision support tool. However, a number of difficulties arise when using RL beyond benchmark environments, such as specifying the reward function, choosing an appropriate state representation and evaluating the learned policy.

Variational quantum circuits have recently gained popularity as quantum machine learning models. While considerable effort has been invested to train them in supervised and unsupervised learning settings, relatively little attention has been given to their potential use in reinforcement learning. In this work, we leverage the understanding of quantum policy gradient algorithms in a number of ways. First, we investigate how to construct and train reinforcement learning policies based on variational quantum circuits. We propose several designs for quantum policies, provide their learning algorithms, and test their performance on classical benchmarking environments. Second, we show the existence of task environments with a provable separation in performance between quantum learning agents and any polynomial-time classical learner, conditioned on the widely-believed classical hardness of the discrete logarithm problem. We also consider more natural settings, in which we show an empirical quantum advantage of our quantum policies over standard neural-network policies. Our results constitute a first step towards establishing a practical near-term quantum advantage in a reinforcement learning setting. Additionally, we believe that some of our design choices for variational quantum policies may also be beneficial to other models based on variational quantum circuits, such as quantum classifiers and quantum regression models.

Crop type maps are frequently generated using remotely sensed data acquired by sensors mounted on satellites, manned aircraft or unmanned aerial vehicles (UAVs or'drones'), the most popular being multispectral sensors mounted on satellites. Aerial multispectral sensors are more frequently employed where imagery with very high spatial resolution is required. However, the use of Lidar data for crop type mapping is still uncommon. This article outlines research done on creating crop type maps using Lidar, Sentinel-2 and aerial data along with several machine learning classification algorithms for differentiating four crop types in an intensively cultivated area. Lidar data is becoming ever-more widely available as more aerial surveys are conducted, UAV-Lidar sensors are becoming more prevalent and Earth observation satellites are being fitted with Lidar sensors.

This story is part of a series I am creating about neural networks. This chapter is dedicated to a type of neural network known as adaptive linear unit (adaline), whose creation is attributed to Bernard Widrow and Ted Hoff shortly after the perceptron network. Although both adaline and the perceptron were inspired by the McCulloch and Pitts neuron, there are some subtle but significant differences between both networks, some of them having established the foundations of training algorithms in current neural network architectures. Ted Hoff was Widrow's doctorate student (fun fact: he was also Intel's employee number 12). Their partnership during this time resulted in adaline neuron's work, published in 1960.

In supervised machine learning, you usually have an input X, which goes into your prediction function to get your Y . You can then compare your prediction with the true value Y. This gives you your cost which you use to update the parameters θ. Sentiment analysis (also known as opinion mining or emotion AI) refers to the use of natural language processing, text analysis, computational linguistics, and biometrics to systematically identify, extract, quantify, and study affective states and subjective information. So, let's start sentiment analysis using Logistic Regression We will be using the sample twitter data set for this exercise.

Understanding generalization and estimation error of estimators for simple models such as linear and generalized linear models has attracted a lot of attention recently. This is in part due to an interesting observation made in machine learning community that highly over-parameterized neural networks achieve zero training error, and yet they are able to generalize well over the test samples. This phenomenon is captured by the so called double descent curve, where the generalization error starts decreasing again after the interpolation threshold. A series of recent works tried to explain such phenomenon for simple models. In this work, we analyze the asymptotics of estimation error in ridge estimators for convolutional linear models. These convolutional inverse problems, also known as deconvolution, naturally arise in different fields such as seismology, imaging, and acoustics among others. Our results hold for a large class of input distributions that include i.i.d. features as a special case. We derive exact formulae for estimation error of ridge estimators that hold in a certain high-dimensional regime. We show the double descent phenomenon in our experiments for convolutional models and show that our theoretical results match the experiments.