Predicting the labelling of a graph via minimum p-seminorm interpolation

We study the problem of predicting the labelling of a graph. The graph is given and a trial sequence of (vertex,label) pairs is then incrementally revealed to the learner. On each trial a vertex is queried and the learner predicts a boolean label. The true label is then returned. The learner’s goal is to minimise mistaken predictions. We propose minimum p-seminorm interpolation to solve this problem. To this end we give a p-seminorm on the space of graph labellings. Thus on every trial we predict using the labelling which minimises the p-seminorm and is also consistent with the revealed (vertex, label) pairs. When p = 2 this is the harmonic energy minimisation procedure of [22], also called (Laplacian) interpolated regularisation in [1]. In the limit as p → 1 this is equivalent to predicting with a label-consistent mincut. We give mistake bounds relative to a label-consistent mincut and a resistive cover of the graph. We say an edge is cut with respect to a labelling if the connected vertices have disagreeing labels. We find that minimising the p-seminorm with p = 1 + ɛ where ɛ → 0 as the graph diameter D → ∞ gives a bound of O(Φ 2 log D) versus a bound of O(ΦD) when p = 2 where Φ is the number of cut edges.

Approximate Newton Methods for Policy Search in Markov Decision Processes

Approximate Newton methods are standard optimization tools which aim to maintain the benefits of Newton's method, such as a fast rate of convergence, while alleviating its drawbacks, such as computationally expensive calculation or estimation of the inverse Hessian. In this work we investigate approximate Newton methods for policy optimization in Markov decision processes (MDPs). We first analyse the structure of the Hessian of the total expected reward, which is a standard objective function for MDPs. We show that, like the gradient, the Hessian exhibits useful structure in the context of MDPs and we use this analysis to motivate two Gauss-Newton methods for MDPs. Like the Gauss- Newton method for non-linear least squares, these methods drop certain terms in the Hessian. The approximate Hessians possess desirable properties, such as negative definiteness, and we demonstrate several important performance guarantees including guaranteed ascent directions, invariance to affine transformation of the parameter space and convergence guarantees. We finally provide a unifying perspective of key policy search algorithms, demonstrating that our second Gauss- Newton algorithm is closely related to both the EM-algorithm and natural gradient ascent applied to MDPs, but performs significantly better in practice on a range of challenging domains

Si/SiGe bound-to-continuum quantum cascade emitters

Si/SiGe bound-to-continuum quantum cascade emitters designed by self-consistent 6-band k.p modeling and grown by low energy plasma enhanced chemical vapour deposition are presented demonstrating electroluminescence between 1.5 and 3 THz. The electroluminescence is Stark shifted by an electric field and demonstrates polarized emission consistent with the design. Transmission electron microscopy and x-ray diffraction are also presented to characterize the thick heterolayer structure

Exploiting structure defined by data in machine learning: some new analyses

This thesis offers some new analyses and presents some new methods for learning in the context of exploiting structure defined by data – for example, when a data distribution has a submanifold support, exhibits cluster structure or exists as an object such as a graph. 1. We present a new PAC-Bayes analysis of learning in this context, which is sharp and in some ways presents a better solution than uniform convergence methods. The PAC-Bayes prior over a hypothesis class is defined in terms of the unknown true risk and smoothness of hypotheses w.r.t. the unknown data-generating distribution. The analysis is “localized” in the sense that complexity of the model enters not as the complexity of an entire hypothesis class, but focused on functions of ultimate interest. Such bounds are derived for various algorithms including SVMs. 2. We consider an idea similar to the p-norm Perceptron for building classifiers on graphs. We define p-norms on the space of functions over graph vertices and consider interpolation using the pnorm as a smoothness measure. The method exploits cluster structure and attains a mistake bound logarithmic in the diameter, compared to a linear lower bound for standard methods. 3. Rademacher complexity is related to cluster structure in data, quantifying the notion that when data clusters we can learn well with fewer examples. In particular we relate transductive learning to cluster structure in the empirical resistance metric. 4. Typical methods for learning over a graph do not scale well in the number of data points – often a graph Laplacian must be inverted which becomes computationally intractable for large data sets. We present online algorithms which, by simplifying the graph in principled way, are able to exploit the structure while remaining computationally tractable for large datasets. We prove state-of-the-art performance guarantees

Depression, Anxiety, Post-traumatic Stress Disorder and a History of Pervasive Gender-Based Violence Among Women Asylum Seekers Who Have Undergone Female Genital Mutilation/Cutting: A Retrospective Case Review

We sought to evaluate the frequency of anxiety, depression, PTSD, and any experiences of violence in women who had undergone Female Genital Mutilation/Cutting (FGM/C) and were seeking asylum in the United States. We undertook a retrospective qualitative descriptive study of FGM/C cases seen in an asylum clinic over a 2-year period. Standardized questionnaires provided quantitative scores for anxiety, depression and PTSD. Clients’ personal and physician medical affidavits were analyzed for experiences of violence. Of the 13 cases, anxiety and depression were exhibited by 92 and 100% of women, while all seven women screened for PTSD had symptoms. Qualitative analysis revealed extensive violence perpetrated against these women, demonstrating that FGM/C is only part of the trauma experienced. The high level of mental health disorders and endured violence has implications for providers working with FGM/C survivors and indicates the need for accessible mental health services and trauma-informed care

Ge-on-Si single-photon avalanche diode detectors: design, modeling, fabrication, and characterization at wavelengths 1310 and 1550 nm

The design, modeling, fabrication, and characterization of single-photon avalanche diode detectors with an epitaxial Ge absorption region grown directly on Si are presented. At 100 K, a single-photon detection efficiency of 4% at 1310 nm wavelength was measured with a dark count rate of ~ 6 megacounts/s, resulting in the lowest reported noise-equivalent power for a Ge-on-Si single-photon avalanche diode detector (1×10-14 WHz-1/2). The first report of 1550 nm wavelength detection efficiency measurements with such a device is presented. A jitter of 300 ps was measured, and preliminary tests on after-pulsing showed only a small increase (a factor of 2) in the normalized dark count rate when the gating frequency was increased from 1 kHz to 1 MHz. These initial results suggest that optimized devices integrated on Si substrates could potentially provide performance comparable to or better than that of many commercially available discrete technologies

Successful use of axonal transport for drug delivery by synthetic molecular vehicles

We report the use of axonal transport to achieve intraneural drug delivery. We constructed a novel tripartite complex of an axonal transport facilitator conjugated to a linker molecule bearing up to a hundred reversibly attached drug molecules. The complex efficiently enters nerve terminals after intramuscular or intradermal administration and travels within axonal processes to neuron cell bodies. The tripartite agent provided 100-fold amplification of saturable neural uptake events, delivering multiple drug molecules per complex. _In vivo_, analgesic drug delivery to systemic and to non-targeted neural tissues was greatly reduced compared to existing routes of administration, thus exemplifying the possibility of specific nerve root targeting and effectively increasing the potency of the candidate drug gabapentin 300-fold relative to oral administration