Few-shot classification is a challenging problem as only very few training examples are given for each new task. One of the effective research lines to address this challenge focuses on learning deep representations driven by a similarity measure between a query image and few support images of some class. Statistically, this amounts to measure the dependency of image features, viewed as random vectors in a high-dimensional embedding space. Previous methods either only use marginal distributions without considering joint distributions, suffering from limited representation capability, or are computationally expensive though harnessing joint distributions. In this paper, we propose a deep Brownian Distance Covariance (DeepBDC) method for few-shot classification. The central idea of DeepBDC is to learn image representations by measuring the discrepancy between joint characteristic functions of embedded features and product of the marginals. As the BDC metric is decoupled, we formulate it as a highly modular and efficient layer. Furthermore, we instantiate DeepBDC in two different few-shot classification frameworks. We make experiments on six standard few-shot image benchmarks, covering general object recognition, fine-grained categorization and cross-domain classification. Extensive evaluations show our DeepBDC significantly outperforms the counterparts, while establishing new state-of-the-art results. The source code is available at http://www.peihuali.org/DeepBDC

We develop new upper and lower bounds on the $\varepsilon$-entropy of a unit ball in a reproducing kernel Hilbert space induced by some Mercer kernel $K$. Our bounds are based on the behaviour of eigenvalues of a corresponding integral operator. In our approach we exploit an ellipsoidal structure of a unit ball in RKHS and a previous work on covering numbers of an ellipsoid in the euclidean space obtained by Dumer, Pinsker and Prelov. We present a number of applications of our main bound, such as its tightness for a practically important case of the Gaussian kernel. Further, we develop a series of lower bounds on the $\varepsilon$-entropy that can be established from a connection between covering numbers of a ball in RKHS and a quantization of a Gaussian Random Field that corresponds to the kernel $K$ by the Kosambi-Karhunen-Lo\`eve transform.

The diagnostics plot for this particular model shows a decently good fit . When being used for prediction, it followed the real trend closely. And since our focus is on the estimates/coefficients of the bool_promotion variable, I considered this model good enough to be used in our analysis. As we can see from the model summary, our bool_promotion variable is significant, meaning it's showed to affect sales of grocery I at store 1, and in this case, positively. Having promotions added more than 500 units to the sales for this given combination. Having figured out the pipeline throughout these steps, I automated this process for other store-city-product combinations with auto_arima(), which helps us identify the best fit set of orders, record these orders, as well as coefficients. First, I created a helper function to identify the necessary parameters and train the auto_arima(). One parameter that appeared tricky to me was parameter m, which is the period for seasonal differencing.

Rattle and R deliver a very sophisticated data mining environment. Data Mining with Rattle is a unique course that instructs with respect to both the concepts of data mining, as well as to the "hands-on" use of a popular, contemporary data mining software tool, "Data Miner," also known as the'Rattle' package in R software. Rattle is a popular GUI-based software tool which'fits on top of' R software. The course focuses on life-cycle issues, processes, and tasks related to supporting a'cradle-to-grave' data mining project. These include: data exploration and visualization; testing data for random variable family characteristics and distributional assumptions; transforming data by scale or by data type; performing cluster analyses; creating, analyzing and interpreting association rules; and creating and evaluating predictive models that may utilize: regression; generalized linear modeling (GLMs); decision trees; recursive partitioning; random forests; boosting; and/or support vector machine (SVM) paradigms. It is both a conceptual and a practical course as it teaches and instructs about data mining, and provides ample demonstrations of conducting data mining tasks using the Rattle R package.

Traditionally, supervised machine learning algorithms are trained based on past data under the assumption that the past data is representative of the future. However, machine learning algorithms are increasingly being used in settings where the output of the algorithm changes the environment and hence, the data distribution. Indeed, online labor markets (Anagnostopoulos et al., 2018; Horton, 2010), predictive policing (Lum and Isaac, 2016), on-street parking (Dowling et al., 2020; Pierce and Shoup, 2018), and vehicle sharing markets (Banerjee et al., 2015) are all examples of real-world settings in which the algorithm's decisions change the underlying data distribution due to the fact that the algorithm interacts with strategic users. To address this problem, the machine learning community introduced the problem of performative prediction which models the data distribution as being decision-dependent thereby accounting for feedback induced distributional shift (Brown et al., 2020; Drusvyatskiy and Xiao, 2020; Mendler-Dünner et al., 2020; Miller et al., 2021; Perdomo et al., 2020). With the exception of (Brown et al., 2020), this work has focused on static environments. In many of the aforementioned application domains, however, the underlying data distribution also may have memory or even be changing dynamically in time. When a decision-making mechanism is announced it may take time to see the full effect of the decision as the environment and strategic data sources respond given their prior history or interactions. For example, many municipalities announce quarterly a new quasi-static set of prices for on-street parking. In this scenario, the institution may adjust parking rates for certain blocks in order to to achieve a desired occupancy range to reduce cruising phenomena and increase business district vitality (Dowling et al., 2017; Fiez et al., 2018; Pierce and Shoup, 2013; Shoup, 2006).

Time series modeling is a very common technique throughout many areas of machine learning. However, many standard recurrent models are known to be susceptible to problems such as the vanishing gradient [Pascanu et al., 2013] or the extreme sensitivity of chaotic systems to their parameterization [Wiggins et al., 2003]. To counter these issues reservoir computing (RC) techniques were introduced as recurrent models which can be trained without requiring gradient-based approaches [Lukoševičius and Jaeger, 2009]. Independently proposed as echo state networks (ESNs) [Jaeger, 2001] and liquid state machines (LSMs) [Maass et al., 2002], these architectures are based on the expansion of the input data using a fixed random internal layer, known as the reservoir, and the subsequent mapping of the reservoir to match an output.

Machine Learning (ML) for Ligand Based Virtual Screening (LB-VS) is an important in-silico tool for discovering new drugs in a faster and cost-effective manner, especially for emerging diseases such as COVID-19. In this paper, we propose a general-purpose framework combining a classical Support Vector Classifier (SVC) algorithm with quantum kernel estimation for LB-VS on real-world databases, and we argue in favor of its prospective quantum advantage. Indeed, we heuristically prove that our quantum integrated workflow can, at least in some relevant instances, provide a tangible advantage compared to state-of-art classical algorithms operating on the same datasets, showing strong dependence on target and features selection method. Finally, we test our algorithm on IBM Quantum processors using ADRB2 and COVID-19 datasets, showing that hardware simulations provide results in line with the predicted performances and can surpass classical equivalents.

Regularization is a fundamental technique to prevent over-fitting and to improve generalization performances by constraining a model's complexity. Current Deep Networks heavily rely on regularizers such as Data-Augmentation (DA) or weight-decay, and employ structural risk minimization, i.e. cross-validation, to select the optimal regularization hyper-parameters. In this study, we demonstrate that techniques such as DA or weight decay produce a model with a reduced complexity that is unfair across classes. The optimal amount of DA or weight decay found from cross-validation leads to disastrous model performances on some classes e.g. on Imagenet with a resnet50, the "barn spider" classification test accuracy falls from $68\%$ to $46\%$ only by introducing random crop DA during training. Even more surprising, such performance drop also appears when introducing uninformative regularization techniques such as weight decay. Those results demonstrate that our search for ever increasing generalization performance -- averaged over all classes and samples -- has left us with models and regularizers that silently sacrifice performances on some classes. This scenario can become dangerous when deploying a model on downstream tasks e.g. an Imagenet pre-trained resnet50 deployed on INaturalist sees its performances fall from $70\%$ to $30\%$ on class \#8889 when introducing random crop DA during the Imagenet pre-training phase. Those results demonstrate that designing novel regularizers without class-dependent bias remains an open research question.

We consider the problem of learning high dimensional polynomial transformations of Gaussians. Given samples of the form $p(x)$, where $x\sim N(0, \mathrm{Id}_r)$ is hidden and $p: \mathbb{R}^r \to \mathbb{R}^d$ is a function where every output coordinate is a low-degree polynomial, the goal is to learn the distribution over $p(x)$. This problem is natural in its own right, but is also an important special case of learning deep generative models, namely pushforwards of Gaussians under two-layer neural networks with polynomial activations. Understanding the learnability of such generative models is crucial to understanding why they perform so well in practice. Our first main result is a polynomial-time algorithm for learning quadratic transformations of Gaussians in a smoothed setting. Our second main result is a polynomial-time algorithm for learning constant-degree polynomial transformations of Gaussian in a smoothed setting, when the rank of the associated tensors is small. In fact our results extend to any rotation-invariant input distribution, not just Gaussian. These are the first end-to-end guarantees for learning a pushforward under a neural network with more than one layer. Along the way, we also give the first polynomial-time algorithms with provable guarantees for tensor ring decomposition, a popular generalization of tensor decomposition that is used in practice to implicitly store large tensors.

Over the last few years, deep learning has grown in popularity for speaker verification, identification, and diarization. Inarguably, a significant part of this success is due to the demonstrated effectiveness of their speaker representations. These, however, are heavily dependent on large amounts of annotated data and can be sensitive to new domains. This study proposes an entirely unsupervised deep-learning model for speaker diarization. Specifically, the study focuses on generating high-quality neural speaker representations without any annotated data, as well as on estimating secondary hyperparameters of the model without annotations. The speaker embeddings are represented by an encoder trained in a self-supervised fashion using pairs of adjacent segments assumed to be of the same speaker. The trained encoder model is then used to self-generate pseudo-labels to subsequently train a similarity score between different segments of the same call using probabilistic linear discriminant analysis (PLDA) and further to learn a clustering stopping threshold. We compared our model to state-of-the-art unsupervised as well as supervised baselines on the CallHome benchmarks. According to empirical results, our approach outperforms unsupervised methods when only two speakers are present in the call, and is only slightly worse than recent supervised models.