Due to the expanding scope of machine learning (ML) to the fields of sensor networking, cooperative robotics and many other multi-agent systems, distributed deployment of inference algorithms has received a lot of attention. These algorithms involve collaboratively learning unknown parameters from dispersed data collected by multiple agents. There are two competing aspects in such algorithms, namely, intra-agent computation and inter-agent communication. Traditionally, algorithms are designed to perform both synchronously. However, certain circumstances need frugal use of communication channels as they are either unreliable, time-consuming, or resource-expensive. In this paper, we propose gossip-based asynchronous communication to leverage fast computations and reduce communication overhead simultaneously. We analyze the effects of multiple (local) intra-agent computations by the active agents between successive inter-agent communications. For local computations, Bayesian sampling via unadjusted Langevin algorithm (ULA) MCMC is utilized. The communication is assumed to be over a connected graph (e.g., as in decentralized learning), however, the results can be extended to coordinated communication where there is a central server (e.g., federated learning). We theoretically quantify the convergence rates in the process. To demonstrate the efficacy of the proposed algorithm, we present simulations on a toy problem as well as on real world data sets to train ML models to perform classification tasks. We observe faster initial convergence and improved performance accuracy, especially in the low data range. We achieve on average 78% and over 90% classification accuracy respectively on the Gamma Telescope and mHealth data sets from the UCI ML repository.

This manuscript is technical memoir about my work at Stanford and Microsoft Research. Included are fundamental concepts central to machine learning and artificial intelligence, applications of these concepts, and stories behind their creation.

Abstract: Recent strides in the field of neural computation has seen the adoption of Winner-Take-All (WTA) circuits to facilitate the unification of hierarchical Bayesian inference and spiking neural networks as a neurobiologically plausible model of information processing. However, researchers have not yet reached consensus about how best to translate the stochastic responses from these networks into discrete decisions, a process known as population decoding. Despite being an often underexamined part of SNNs, in this work we show that population decoding has a significanct impact on the classification performance of WTA networks. For this purpose, we apply a WTA network to the problem of cancer subtype diagnosis from multi-omic data, using datasets from The Cancer Genome Atlas (TCGA). In doing so we utilise a novel implementation of gene similarity networks, a feature encoding technique based on Kohoen's self-organising map algorithm. We further show that the impact of selecting certain population decoding methods is amplified when facing imbalanced datasets. Multi-omics data integration in cancer diagnosis Alternatively, some research focuses on the timedependent refers to the integration of information from various relationship of spiking neurons, for biological "omics" e.g., genomics, transcriptomics, instance by weighting neuron responses more highly metabolomics, to provide a more comprehensive based on how quickly they fire (Grün & Rotter, 2010; understanding of the molecular landscape of cancer. In order to extract information from SNNs, we neurobiologically inspired method of information examine the spikes generated by a population of processing which aim to solve tasks using plausible neurons in response to a stimulus.

This approach lacks the extra information on individual systems with interval-censored data and time-varying weapon system characteristics. A recent method introduced the covariates. We analyze and benchmark our approach, Weibull-Cox Bayesian Neural Network tested on several LaplaceNN, on synthetic and real datasets with standard weapon systems, albeit requiring a held-out validation set [7]. classification metrics such as Receiver Operating Characteristic Moreover, while understanding the population reliability trends (ROC) Area Under Curve (AUC) Precision-Recall (PR) AUC, via a Weibull distribution is informative, this formulation does and reliability curve visualizations.

Meta reinforcement learning (meta-RL) methods such as RL$^2$ have emerged as promising approaches for learning data-efficient RL algorithms tailored to a given task distribution. However, these RL algorithms struggle with long-horizon tasks and out-of-distribution tasks since they rely on recurrent neural networks to process the sequence of experiences instead of summarizing them into general RL components such as value functions. Moreover, even transformers have a practical limit to the length of histories they can efficiently reason about before training and inference costs become prohibitive. In contrast, traditional RL algorithms are data-inefficient since they do not leverage domain knowledge, but they do converge to an optimal policy as more data becomes available. In this paper, we propose RL$^3$, a principled hybrid approach that combines traditional RL and meta-RL by incorporating task-specific action-values learned through traditional RL as an input to the meta-RL neural network. We show that RL$^3$ earns greater cumulative reward on long-horizon and out-of-distribution tasks compared to RL$^2$, while maintaining the efficiency of the latter in the short term. Experiments are conducted on both custom and benchmark discrete domains from the meta-RL literature that exhibit a range of short-term, long-term, and complex dependencies.

Spatial perception is a key task in several machine intelligence applications such as robotics and computer vision. In general, it involves the nonlinear estimation of hidden variables that represent the system's state. However, in the presence of measurement outliers, the standard nonlinear least squared formulation results in poor estimates. Several methods have been considered in the literature to improve the reliability of the estimation process. Most methods are based on heuristics since guaranteed global robust estimation is not generally practical due to high computational costs. Recently general purpose robust estimation heuristics have been proposed that leverage existing non-minimal solvers available for the outlier-free formulations without the need for an initial guess. In this work, we propose three Bayesian heuristics that have similar structures. We evaluate these heuristics in practical scenarios to demonstrate their merits in different applications including 3D point cloud registration, mesh registration and pose graph optimization. The general computational advantages our proposals offer make them attractive candidates for spatial perception tasks.

Large-scale discrete fracture network (DFN) simulators are standard fare for studies involving the sub-surface transport of particles since direct observation of real world underground fracture networks is generally infeasible. While these simulators have seen numerous successes over several engineering applications, estimations on quantities of interest (QoI) - such as breakthrough time of particles reaching the edge of the system - suffer from a two distinct types of uncertainty. A run of a DFN simulator requires several parameter values to be set that dictate the placement and size of fractures, the density of fractures, and the overall permeability of the system; uncertainty on the proper parameter choices will lead to some amount of uncertainty in the QoI, called epistemic uncertainty. Furthermore, since DFN simulators rely on stochastic processes to place fractures and govern flow, understanding how this randomness affects the QoI requires several runs of the simulator at distinct random seeds. The uncertainty in the QoI attributed to different realizations (i.e. different seeds) of the same random process leads to a second type of uncertainty, called aleatoric uncertainty. In this paper, we perform a Sensitivity Analysis, which directly attributes the uncertainty observed in the QoI to the epistemic uncertainty from each input parameter and to the aleatoric uncertainty. We make several design choices to handle an observed heteroskedasticity in DFN simulators, where the aleatoric uncertainty changes for different inputs, since the quality makes several standard statistical methods inadmissible. Beyond the specific takeaways on which input variables affect uncertainty the most for DFN simulators, a major contribution of this paper is the introduction of a statistically rigorous workflow for characterizing the uncertainty in DFN flow simulations that exhibit heteroskedasticity.

Diffusion models are a class of flexible generative models trained with an approximation to the log-likelihood objective. However, most use cases of diffusion models are not concerned with likelihoods, but instead with downstream objectives such as human-perceived image quality or drug effectiveness. In this paper, we investigate reinforcement learning methods for directly optimizing diffusion models for such objectives. We describe how posing denoising as a multi-step decisionmaking problem enables a class of policy gradient algorithms, which we refer to as denoising diffusion policy optimization (DDPO), that are more effective than alternative reward-weighted likelihood approaches. Empirically, DDPO can adapt text-to-image diffusion models to objectives that are difficult to express via prompting, such as image compressibility, and those derived from human feedback, such as aesthetic quality. Finally, we show that DDPO can improve prompt-image alignment using feedback from a vision-language model without the need for additional data collection or human annotation. The project's website can be found at Diffusion probabilistic models (Sohl-Dickstein et al., 2015) have recently emerged as the de facto standard for generative modeling in continuous domains. The key idea behind diffusion models is to iteratively transform a simple prior distribution into a target distribution by applying a sequential denoising process. This procedure is conventionally motivated as a maximum likelihood estimation problem, with the objective derived as a variational lower bound on the log-likelihood of the training data. However, most use cases of diffusion models are not directly concerned with likelihoods, but instead with downstream objective such as human-perceived image quality or drug effectiveness.

Sparse Bayesian Learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. The hyperparameters in SBL models are crucial for the model's performance, but they are often difficult to estimate due to the non-convexity and the high-dimensionality of the associated objective function. This paper presents a comprehensive framework for hyperparameter estimation in SBL models, encompassing well-known algorithms such as the expectation-maximization (EM), MacKay, and convex bounding (CB) algorithms. These algorithms are cohesively interpreted within an alternating minimization and linearization (AML) paradigm, distinguished by their unique linearized surrogate functions. Additionally, a novel algorithm within the AML framework is introduced, showing enhanced efficiency, especially under low signal noise ratios. This is further improved by a new alternating minimization and quadratic approximation (AMQ) paradigm, which includes a proximal regularization term. The paper substantiates these advancements with thorough convergence analysis and numerical experiments, demonstrating the algorithm's effectiveness in various noise conditions and signal-to-noise ratios.

We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the covariance of a Gaussian up to spectral error $\alpha$ requires $\tilde{\Omega}\left(\frac{d^{3/2}}{\alpha \varepsilon} + \frac{d}{\alpha^2}\right)$ samples, which is tight up to logarithmic factors. This result improves over previous work which established this for $\alpha \le O\left(\frac{1}{\sqrt{d}}\right)$, and is also simpler than previous work. Next, we prove that estimating the mean of a heavy-tailed distribution with bounded $k$th moments requires $\tilde{\Omega}\left(\frac{d}{\alpha^{k/(k-1)} \varepsilon} + \frac{d}{\alpha^2}\right)$ samples. Previous work for this problem was only able to establish this lower bound against pure differential privacy, or in the special case of $k = 2$. Our techniques follow the method of fingerprinting and are generally quite simple. Our lower bound for heavy-tailed estimation is based on a black-box reduction from privately estimating identity-covariance Gaussians. Our lower bound for covariance estimation utilizes a Bayesian approach to show that, under an Inverse Wishart prior distribution for the covariance matrix, no private estimator can be accurate even in expectation, without sufficiently many samples.