The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICA

We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider the case that the observed views are a nonlinear mixing of component-wise corruptions of the sources. When the views are considered separately, this reduces to nonlinear Independent Component Analysis (ICA) for which it is provably impossible to undo the mixing. We present novel identifiability proofs that this is possible when the multiple views are considered jointly, showing that the mixing can theoretically be undone using function approximators such as deep neural networks. In contrast to known identifiability results for nonlinear ICA, we prove that independent latent sources with arbitrary mixing can be recovered as long as multiple, sufficiently different noisy views are available

On Maximum Entropy and Inference

Maximum Entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a model from data, that affords predictions on all other (dependent) variables. Conversely, maximum entropy can be invoked to retrieve the relevant variables (sufficient statistics) directly from the data, once a model is identified by Bayesian model selection. We explore this approach in the case of spin models with interactions of arbitrary order, and we discuss how relevant interactions can be inferred. In this perspective, the dimensionality of the inference problem is not set by the number of parameters in the model, but by the frequency distribution of the data. We illustrate the method showing its ability to recover the correct model in a few prototype cases and discuss its application on a real dataset.Comment: 16 pages, 4 figure

Loss of matrix metalloproteinase 2 in platelets reduces arterial thrombosis in vivo

Platelet activation at a site of vascular injury is essential for the arrest of bleeding; however, excessive platelet activation at a site of arterial damage can result in the unwarranted formation of arterial thrombi, precipitating acute myocardial infarction, or ischemic stroke. Activation of platelets beyond the purpose of hemostasis may occur when substances facilitating thrombus growth and stability accumulate. Human platelets contain matrix metalloproteinase 2 (MMP-2) and release it upon activation. Active MMP-2 amplifies the platelet aggregation response to several agonists by potentiating phosphatidylinositol 3-kinase activation. Using several in vivo thrombosis models, we show that the inactivation of the MMP-2 gene prevented thrombosis induced by weak, but not strong, stimuli in mice but produced only a moderate prolongation of the bleeding time. Moreover, using cross-transfusion experiments and wild-type/MMP-2−/− chimeric mice, we show that it is platelet-derived MMP-2 that facilitates thrombus formation. Finally, we show that platelets activated by a mild vascular damage induce thrombus formation at a downstream arterial injury site by releasing MMP-2. Thus, platelet-derived MMP-2 plays a crucial role in thrombus formation by amplifying the response of platelets to weak activating stimuli. These findings open new possibilities for the prevention of thrombosis by the development of MMP-2 inhibitors

Hyperglycemia-Induced Platelet Activation in Type 2 Diabetes Is Resistant to Aspirin but Not to a Nitric Oxide–Donating Agent

OBJECTIVE: Acute, short-term hyperglycemia enhances high shear stress-induced platelet activation in type 2 diabetes. Several observations suggest that platelets in type 2 diabetes are resistant to inhibition by aspirin. Our aim was to assess comparatively the effect of aspirin, a nitric oxide-donating agent (NCX 4016), their combination, or placebo on platelet activation induced by acute hyperglycemia in type 2 diabetes. RESEARCH DESIGN AND METHODS: In a double-blind, placebo-controlled, randomized trial, 40 type 2 diabetic patients were allocated to 100 mg aspirin once daily, 800 mg NCX 4016 b.i.d., both of them, or placebo for 15 days. On day 15, 1 h after the morning dose, a 4-h hyperglycemic clamp (plasma glucose 13.9 mmol/l) was performed, and blood samples were collected before and immediately after it for platelet activation and cyclooxygenase-1 (COX-1) inhibition studies. RESULTS Acute hyperglycemia enhanced shear stress-induced platelet activation in placebo-treated patients (basal closure time 63 +/- 7.1 s, after hyperglycemia 49.5 +/- 1.4 s, -13.5 +/- 6.3 s, P < 0.048). Pretreatment with aspirin, despite full inhibition of platelet COX-1, did not prevent it (-12.7 +/- 6.9 s, NS vs. placebo). On the contrary, pretreatment with the NO donor NCX 4016, alone or in combination with aspirin, suppressed platelet activation induced by acute hyperglycemia (NCX 4016 +10.5 +/- 8.3 s; NCX 4016 plus aspirin: +12.0 +/- 10.7 s, P < 0.05 vs. placebo for both). Other parameters of shear stress-dependent platelet activation were also more inhibited by NCX 4016 than by aspirin, despite lesser inhibition of COX-1. CONCLUSIONS: Acute hyperglycemia-induced enhancement of platelet activation is resistant to aspirin; a NO-donating agent suppresses it. Therapeutic approaches aiming at a wider platelet inhibitory action than that exerted by aspirin may prove useful in patients with type 2 diabetes

Learning Identifiable Representations: Independent Influences and Multiple Views

Intelligent systems, whether biological or artificial, perceive unstructured information from the world around them: deep neural networks designed for object recognition receive collections of pixels as inputs; living beings capture visual stimuli through photoreceptors that convert incoming light into electrical signals. Sophisticated signal processing is required to extract meaningful features (e.g., the position, dimension, and colour of objects in an image) from these inputs: this motivates the field of representation learning. But what features should be deemed meaningful, and how to learn them? We will approach these questions based on two metaphors. The first one is the cocktail-party problem, where a number of conversations happen in parallel in a room, and the task is to recover (or separate) the voices of the individual speakers from recorded mixtures—also termed blind source separation. The second one is what we call the independent-listeners problem: given two listeners in front of some loudspeakers, the question is whether, when processing what they hear, they will make the same information explicit, identifying similar constitutive elements. The notion of identifiability is crucial when studying these problems, as it specifies suitable technical assumptions under which representations are uniquely determined, up to tolerable ambiguities like latent source reordering. A key result of this theory is that, when the mixing is nonlinear, the model is provably non-identifiable. A first question is, therefore, under what additional assumptions (ideally as mild as possible) the problem becomes identifiable; a second one is, what algorithms can be used to estimate the model. The contributions presented in this thesis address these questions and revolve around two main principles. The first principle is to learn representation where the latent components influence the observations independently. Here the term “independently” is used in a non-statistical sense—which can be loosely thought of as absence of fine-tuning between distinct elements of a generative process. The second principle is that representations can be learned from paired observations or views, where mixtures of the same latent variables are observed, and they (or a subset thereof) are perturbed in one of the views—also termed multi-view setting. I will present work characterizing these two problem settings, studying their identifiability and proposing suitable estimation algorithms. Moreover, I will discuss how the success of popular representation learning methods may be explained in terms of the principles above and describe an application of the second principle to the statistical analysis of group studies in neuroimaging