In this article, we will see how transfer learning can be applied to time series forecasting, and how forecasting models can be trained once on a diverse time series dataset and used later on to obtain forecasts on different datasets without training. We will use the open-source Darts library to do all this with in a few lines of code. A self-contained notebook containing everything needed to reproduce the results is available here. Time series forecasting has numerous applications in supply chain, energy, agriculture, control, IT operations, finance and other domains. For a long time, the best-performing approaches were relatively sophisticated statistical methods such as Exponential Smoothing or ARIMA. However, since recently, machine learning and deep learning have started to outperform these classical approaches on a number of forecasting tasks and competitions.

A rich supply of data and innovative algorithms have made data-driven modeling a popular technique in modern industry. Among various data-driven methods, latent variable models (LVMs) and their counterparts account for a major share and play a vital role in many industrial modeling areas. LVM can be generally divided into statistical learning-based classic LVM and neural networks-based deep LVM (DLVM). We first discuss the definitions, theories and applications of classic LVMs in detail, which serves as both a comprehensive tutorial and a brief application survey on classic LVMs. Then we present a thorough introduction to current mainstream DLVMs with emphasis on their theories and model architectures, soon afterwards provide a detailed survey on industrial applications of DLVMs. The aforementioned two types of LVM have obvious advantages and disadvantages. Specifically, classic LVMs have concise principles and good interpretability, but their model capacity cannot address complicated tasks. Neural networks-based DLVMs have sufficient model capacity to achieve satisfactory performance in complex scenarios, but it comes at sacrifices in model interpretability and efficiency. Aiming at combining the virtues and mitigating the drawbacks of these two types of LVMs, as well as exploring non-neural-network manners to build deep models, we propose a novel concept called lightweight deep LVM (LDLVM). After proposing this new idea, the article first elaborates the motivation and connotation of LDLVM, then provides two novel LDLVMs, along with thorough descriptions on their principles, architectures and merits. Finally, outlooks and opportunities are discussed, including important open questions and possible research directions.

Continuous neural representations have recently emerged as a powerful and flexible alternative to classical discretized representations of signals. However, training them to capture fine details in multi-scale signals is difficult and computationally expensive. Here we propose random weight factorization as a simple drop-in replacement for parameterizing and initializing conventional linear layers in coordinate-based multi-layer perceptrons (MLPs) that significantly accelerates and improves their training. We show how this factorization alters the underlying loss landscape and effectively enables each neuron in the network to learn using its own self-adaptive learning rate. This not only helps with mitigating spectral bias, but also allows networks to quickly recover from poor initializations and reach better local minima. We demonstrate how random weight factorization can be leveraged to improve the training of neural representations on a variety of tasks, including image regression, shape representation, computed tomography, inverse rendering, solving partial differential equations, and learning operators between function spaces.

In this thesis, we research learning algorithms for optimal decision making in two different contexts, Reinforcement Learning in Part I and Auction Design in Part II. Reinforcement learning (RL) is an area of machine learning that is concerned with how an agent should act in an environment in order to maximize its cumulative reward over time. In Chapter 2, inspired by statistical physics, we develop a novel approach to Reinforcement Learning (RL) that not only learns optimal policies with enhanced desirable properties but also sheds new light on maximum entropy RL. In Chapter 3, we tackle the generalization problem in RL using a Bayesian perspective. We show that imperfect knowledge of the environments dynamics effectively turn a fully-observed Markov Decision Process (MDP) into a Partially Observed MDP (POMDP) that we call the Epistemic POMDP. Informed by this observation, we develop a new policy learning algorithm LEEP which has improved generalization properties. Designing an incentive compatible, individually rational auction that maximizes revenue is a challenging and intractable problem. Recently, deep learning based approaches have been proposed to learn optimal auctions from data. While successful, this approach suffers from a few limitations, including sample inefficiency, lack of generalization to new auctions, and training difficulties. In Chapter 4, we construct a symmetry preserving neural network architecture, EquivariantNet, suitable for anonymous auctions. EquivariantNet is not only more sample efficient but is also able to learn auction rules that generalize well to other settings. In Chapter 5, we propose a novel formulation of the auction learning problem as a two player game. The resulting learning algorithm, ALGNet, is easier to train, more reliable and better suited for non stationary settings.

Rice is one of the main staple food in many areas of the world. The quality estimation of rice kernels are crucial in terms of both food safety and socio-economic impact. This was usually carried out by quality inspectors in the past, which may result in both objective and subjective inaccuracies. In this paper, we present an automatic visual quality estimation system of rice kernels, to classify the sampled rice kernels according to their types of flaws, and evaluate their quality via the weight ratios of the perspective kernel types. To compensate for the imbalance of different kernel numbers and classify kernels with multiple flaws accurately, we propose a multi-stage workflow which is able to locate the kernels in the captured image and classify their properties. We define a novel metric to measure the relative weight of each kernel in the image from its area, such that the relative weight of each type of kernels with regard to the all samples can be computed and used as the basis for rice quality estimation. Various experiments are carried out to show that our system is able to output precise results in a contactless way and replace tedious and error-prone manual works.

Mapping behavioral actions to neural activity is a fundamental goal of neuroscience. As our ability to record large neural and behavioral data increases, there is growing interest in modeling neural dynamics during adaptive behaviors to probe neural representations. In particular, neural latent embeddings can reveal underlying correlates of behavior, yet, we lack non-linear techniques that can explicitly and flexibly leverage joint behavior and neural data. Here, we fill this gap with a novel method, CEBRA, that jointly uses behavioral and neural data in a hypothesis- or discovery-driven manner to produce consistent, high-performance latent spaces. We validate its accuracy and demonstrate our tool's utility for both calcium and electrophysiology datasets, across sensory and motor tasks, and in simple or complex behaviors across species. It allows for single and multi-session datasets to be leveraged for hypothesis testing or can be used label-free. Lastly, we show that CEBRA can be used for the mapping of space, uncovering complex kinematic features, and rapid, high-accuracy decoding of natural movies from visual cortex.

Models need to be trained with privacy-preserving learning algorithms to prevent leakage of possibly sensitive information contained in their training data. However, canonical algorithms like differentially private stochastic gradient descent (DP-SGD) do not benefit from model scale in the same way as non-private learning. This manifests itself in the form of unappealing tradeoffs between privacy and utility (accuracy) when using DP-SGD on complex tasks. To remediate this tension, a paradigm is emerging: fine-tuning with differential privacy from a model pretrained on public (i.e., non-sensitive) training data. In this work, we identify an oversight of existing approaches for differentially private fine tuning. They do not tailor the fine-tuning approach to the specifics of learning with privacy. Our main result is to show how carefully selecting the layers being fine-tuned in the pretrained neural network allows us to establish new state-of-the-art tradeoffs between privacy and accuracy. For instance, we achieve 77.9% accuracy for $(\varepsilon, \delta)=(2, 10^{-5})$ on CIFAR-100 for a model pretrained on ImageNet. Our work calls for additional hyperparameter search to configure the differentially private fine-tuning procedure itself.

We revisit the problem of learning mixtures of spherical Gaussians. Given samples from mixture $\frac{1}{k}\sum_{j=1}^{k}\mathcal{N}(\mu_j, I_d)$, the goal is to estimate the means $\mu_1, \mu_2, \ldots, \mu_k \in \mathbb{R}^d$ up to a small error. The hardness of this learning problem can be measured by the separation $\Delta$ defined as the minimum distance between all pairs of means. Regev and Vijayaraghavan (2017) showed that with $\Delta = \Omega(\sqrt{\log k})$ separation, the means can be learned using $\mathrm{poly}(k, d)$ samples, whereas super-polynomially many samples are required if $\Delta = o(\sqrt{\log k})$ and $d = \Omega(\log k)$. This leaves open the low-dimensional regime where $d = o(\log k)$. In this work, we give an algorithm that efficiently learns the means in $d = O(\log k/\log\log k)$ dimensions under separation $d/\sqrt{\log k}$ (modulo doubly logarithmic factors). This separation is strictly smaller than $\sqrt{\log k}$, and is also shown to be necessary. Along with the results of Regev and Vijayaraghavan (2017), our work almost pins down the critical separation threshold at which efficient parameter learning becomes possible for spherical Gaussian mixtures. More generally, our algorithm runs in time $\mathrm{poly}(k)\cdot f(d, \Delta, \epsilon)$, and is thus fixed-parameter tractable in parameters $d$, $\Delta$ and $\epsilon$. Our approach is based on estimating the Fourier transform of the mixture at carefully chosen frequencies, and both the algorithm and its analysis are simple and elementary. Our positive results can be easily extended to learning mixtures of non-Gaussian distributions, under a mild condition on the Fourier spectrum of the distribution.

Self-supervised learning on graphs has recently achieved remarkable success in graph representation learning. With hundreds of self-supervised pretext tasks proposed over the past few years, the research community has greatly developed, and the key is no longer to design more powerful but complex pretext tasks, but to make more effective use of those already on hand. This paper studies the problem of how to automatically, adaptively, and dynamically learn instance-level self-supervised learning strategies for each node from a given pool of pretext tasks. In this paper, we propose a novel multi-teacher knowledge distillation framework for Automated Graph Self-Supervised Learning (AGSSL), which consists of two main branches: (i) Knowledge Extraction: training multiple teachers with different pretext tasks, so as to extract different levels of knowledge with different inductive biases; (ii) Knowledge Integration: integrating different levels of knowledge and distilling them into the student model. Without simply treating different teachers as equally important, we provide a provable theoretical guideline for how to integrate the knowledge of different teachers, i.e., the integrated teacher probability should be close to the true Bayesian class-probability. To approach the theoretical optimum in practice, two adaptive knowledge integration strategies are proposed to construct a relatively "good" integrated teacher. Extensive experiments on eight datasets show that AGSSL can benefit from multiple pretext tasks, outperforming the corresponding individual tasks; by combining a few simple but classical pretext tasks, the resulting performance is comparable to other leading counterparts.

We prove two lower bounds for the complexity of non-log-concave sampling within the framework of Balasubramanian et al. (2022), who introduced the use of Fisher information (FI) bounds as a notion of approximate first-order stationarity in sampling. Our first lower bound shows that averaged LMC is optimal for the regime of large FI by reducing the problem of finding stationary points in non-convex optimization to sampling. Our second lower bound shows that in the regime of small FI, obtaining a FI of at most $\varepsilon^2$ from the target distribution requires $\text{poly}(1/\varepsilon)$ queries, which is surprising as it rules out the existence of high-accuracy algorithms (e.g., algorithms using Metropolis-Hastings filters) in this context.