Impact of regularization on Spectral Clustering

The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et. al (2012). Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the stochastic block model (SBM), and its extensions, previous results on spectral clustering relied on the minimum degree of the graph being sufficiently large for its good performance. By examining the scenario where the regularization parameter $\tau$ is large we show that the minimum degree assumption can potentially be removed. As a special case, for an SBM with two blocks, the results require the maximum degree to be large (grow faster than $\log n$) as opposed to the minimum degree. More importantly, we show the usefulness of regularization in situations where not all nodes belong to well-defined clusters. Our results rely on a `bias-variance'-like trade-off that arises from understanding the concentration of the sample Laplacian and the eigen gap as a function of the regularization parameter. As a byproduct of our bounds, we propose a data-driven technique \textit{DKest} (standing for estimated Davis-Kahan bounds) for choosing the regularization parameter. This technique is shown to work well through simulations and on a real data set.Comment: 37 page

Asthma Across Age : Insights From Primary Care

Peer reviewedPublisher PD

Quantum steering ellipsoids, extremal physical states and monogamy

A Corrigendum for this article has been published in 2015 New J. Phys. 17 019501Any two-qubit state can be faithfully represented by a steering ellipsoid inside the Bloch sphere, but not every ellipsoid inside the Bloch sphere corresponds to a two-qubit state. We give necessary and sufficient conditions for when the geometric data describe a physical state and investigate maximal volume ellipsoids lying on the physical-unphysical boundary. We derive monogamy relations for steering that are strictly stronger than the Coffman-Kundu- Wootters (CKW) inequality for monogamy of concurrence. The CKW result is thus found to follow from the simple perspective of steering ellipsoid geometry. Remarkably, we can also use steering ellipsoids to derive non-trivial results in classical Euclidean geometry, extending Eulers inequality for the circumradius and inradius of a triangle.The EPSRC and the ARC Centre of Excellence grant no. CE110001027. DJ is funded by the Royal Society. TR would like to thank the Leverhulme Trust. SJ acknowledges EPSRC grant EP/ K022512/1

SynthDST: Synthetic Data is All You Need for Few-Shot Dialog State Tracking

In-context learning with Large Language Models (LLMs) has emerged as a promising avenue of research in Dialog State Tracking (DST). However, the best-performing in-context learning methods involve retrieving and adding similar examples to the prompt, requiring access to labeled training data. Procuring such training data for a wide range of domains and applications is time-consuming, expensive, and, at times, infeasible. While zero-shot learning requires no training data, it significantly lags behind the few-shot setup. Thus, `\textit{Can we efficiently generate synthetic data for any dialogue schema to enable few-shot prompting?}' Addressing this question, we propose \method, a data generation framework tailored for DST, utilizing LLMs. Our approach only requires the dialogue schema and a few hand-crafted dialogue templates to synthesize natural, coherent, and free-flowing dialogues with DST annotations. Few-shot learning using data from {\method} results in $4-5$ improvement in Joint Goal Accuracy over the zero-shot baseline on MultiWOZ 2.1 and 2.4. Remarkably, our few-shot learning approach recovers nearly $98$ of the performance compared to the few-shot setup using human-annotated training data. Our synthetic data and code can be accessed at https://github.com/apple/ml-synthdstComment: 9 pages. 4 figures, EACL 2024 main conferenc

5IDER: Unified Query Rewriting for Steering, Intent Carryover, Disfluencies, Entity Carryover and Repair

Providing voice assistants the ability to navigate multi-turn conversations is a challenging problem. Handling multi-turn interactions requires the system to understand various conversational use-cases, such as steering, intent carryover, disfluencies, entity carryover, and repair. The complexity of this problem is compounded by the fact that these use-cases mix with each other, often appearing simultaneously in natural language. This work proposes a non-autoregressive query rewriting architecture that can handle not only the five aforementioned tasks, but also complex compositions of these use-cases. We show that our proposed model has competitive single task performance compared to the baseline approach, and even outperforms a fine-tuned T5 model in use-case compositions, despite being 15 times smaller in parameters and 25 times faster in latency.Comment: Interspeech 202

rac-Diethyl 5-oxo-2-[(2,4,4-trimethyl­pentan-2-yl)amino]-4,5-dihydro­pyrano[3,2-c]chromene-3,4-dicarboxyl­ate

The title compound, C26H33NO7, comprises a racemic mixture of asymmetric mol­ecules containing one stereogenic centre. The dihedral angle between the mean planes of the fused pyran ring and the coumarin ring system is 8.12 (14)°. The mol­ecular structure features a short N—H⋯O contact, which generates an S(6) ring motif. The crystal packing are stabilized by C—H⋯O inter­actions

A Systems Engineering Approach to Modeling and Analysis of Chronic Obstructive Pulmonary Disease (COPD)

Chronic Obstructive Pulmonary Disease (COPD) is a progressive lung disease characterized by airflow limitation. This study develops a systems engineering framework for representing important mechanistic details of COPD in a model of the cardio-respiratory system. In this model, we present the cardio-respiratory system as an integrated biological control system responsible for regulating breathing. Four engineering control system components are considered: sensor, controller, actuator, and the process itself. Knowledge of human anatomy and physiology is used to develop appropriate mechanistic mathematical models for each component. Following a systematic analysis of the computational model, we identify three physiological parameters associated with reproducing clinical manifestations of COPD - changes in the forced expiratory volume (FEV), lung volumes, and pulmonary hypertension. We quantify the changes in these parameters (airway resistance, lung elastance, and pulmonary resistance) as the ones that result in a systemic response that is diagnostic of COPD. A multivariate analysis reveals that the changes in airway resistance have a broad impact on the human cardio-respiratory system, and that the pulmonary circuit is stressed beyond normal under hypoxic environments in most COPD patients.Comment: 25 pages, 15 figure