Transfer learning is essential when sufficient data comes from the source domain, with scarce labeled data from the target domain. We develop estimators that achieve minimax linear risk for linear regression problems under distribution shift. Our algorithms cover different transfer learning settings including covariate shift and model shift. We also consider when data are generated from either linear or general nonlinear models. We show that linear minimax estimators are within an absolute constant of the minimax risk even among nonlinear estimators for various source/target distributions.

We study fast algorithms for statistical regression problems under the strong contamination model, where the goal is to approximately optimize a generalized linear model (GLM) given adversarially corrupted samples. Prior works in this line of research were based on the robust gradient descent framework of Prasad et. al., a first-order method using biased gradient queries, or the Sever framework of Diakonikolas et. al., an iterative outlier-removal method calling a stationary point finder. We present nearly-linear time algorithms for robust regression problems with improved runtime or estimation guarantees compared to the state-of-the-art. For the general case of smooth GLMs (e.g. logistic regression), we show that the robust gradient descent framework of Prasad et. al. can be accelerated, and show our algorithm extends to optimizing the Moreau envelopes of Lipschitz GLMs (e.g. support vector machines), answering several open questions in the literature. For the well-studied case of robust linear regression, we present an alternative approach obtaining improved estimation rates over prior nearly-linear time algorithms. Interestingly, our method starts with an identifiability proof introduced in the context of the sum-of-squares algorithm of Bakshi and Prasad, which achieved optimal error rates while requiring large polynomial runtime and sample complexity. We reinterpret their proof within the Sever framework and obtain a dramatically faster and more sample-efficient algorithm under fewer distributional assumptions.

The first case of neural networks was in 1943, when neurophysiologist Warren McCulloch and mathematician Walter Pitts wrote a paper about neurons, and how they work. They decided to create a model of this using an electrical circuit, and therefore the neural network was born. In 1950, Alan Turing created the world-famous Turing Test. This test is fairly simple for a computer to pass, it has to be able to convince a human that it is a human and not a computer. It was a game which played checkers, created by Arthur Samuel.

I graduated on Warsaw University of Technology with master thesis about text mining topic (intelligent web crawling methods). I work for Polish IT consulting company (Sollers Consulting), where I develop and design various insurance industry related stuff, (one of them is insurance fraud detection platform). From time to time I try to compete in data mining contests (Netflix, competitions on Kaggle and tunedit.org) As far as I remember, the basis of the solution I defined at the very beginning: to create separate predictors for each individual loop and time interval. So my solution required me to build 61x10 610 regression models.

Many scientific datasets are compositional in nature. Important examples include species abundances in ecology, rock compositions in geology, topic compositions in large-scale text corpora, and sequencing count data in molecular biology. Here, we provide a causal view on compositional data in an instrumental variable setting where the composition acts as the cause. Throughout, we pay particular attention to the interpretation of compositional causes from the viewpoint of interventions and crisply articulate potential pitfalls for practitioners. Focusing on modern high-dimensional microbiome sequencing data as a timely illustrative use case, our analysis first reveals that popular one-dimensional information-theoretic summary statistics, such as diversity and richness, may be insufficient for drawing causal conclusions from ecological data. Instead, we advocate for multivariate alternatives using statistical data transformations and regression techniques that take the special structure of the compositional sample space into account. In a comparative analysis on synthetic and semi-synthetic data we show the advantages and limitations of our proposal. We posit that our framework may provide a useful starting point for cause-effect estimation in the context of compositional data.

Recently introduced self-supervised methods for image representation learning provide on par or superior results to their fully supervised competitors, yet the corresponding efforts to explain the self-supervised approaches lag behind. Motivated by this observation, we introduce a novel visual probing framework for explaining the self-supervised models by leveraging probing tasks employed previously in natural language processing. The probing tasks require knowledge about semantic relationships between image parts. Hence, we propose a systematic approach to obtain analogs of natural language in vision, such as visual words, context, and taxonomy. Our proposal is grounded in Marr's computational theory of vision and concerns features like textures, shapes, and lines. We show the effectiveness and applicability of those analogs in the context of explaining self-supervised representations. Our key findings emphasize that relations between language and vision can serve as an effective yet intuitive tool for discovering how machine learning models work, independently of data modality. Our work opens a plethora of research pathways towards more explainable and transparent AI.

We propose a new approach to increase inference performance in environments that require a specific sequence of actions in order to be solved. This is for example the case for maze environments where ideally an optimal path is determined. Instead of learning a policy for a single step, we want to learn a policy that can predict n actions in advance. Our proposed method called policy horizon regression (PHR) uses knowledge of the environment sampled by A2C to learn an n dimensional policy vector in a policy distillation setup which yields n sequential actions per observation. We test our method on the MiniGrid and Pong environments and show drastic speedup during inference time by successfully predicting sequences of actions on a single observation.

Counterfactual explanations and adversarial examples have emerged as critical research areas for addressing the explainability and robustness goals of machine learning (ML). While counterfactual explanations were developed with the goal of providing recourse to individuals adversely impacted by algorithmic decisions, adversarial examples were designed to expose the vulnerabilities of ML models. While prior research has hinted at the commonalities between these frameworks, there has been little to no work on systematically exploring the connections between the literature on counterfactual explanations and adversarial examples. In this work, we make one of the first attempts at formalizing the connections between counterfactual explanations and adversarial examples. More specifically, we theoretically analyze salient counterfactual explanation and adversarial example generation methods, and highlight the conditions under which they behave similarly. Our analysis demonstrates that several popular counterfactual explanation and adversarial example generation methods such as the ones proposed by Wachter et. al. and Carlini and Wagner (with mean squared error loss), and C-CHVAE and natural adversarial examples by Zhao et. al. are equivalent. We also bound the distance between counterfactual explanations and adversarial examples generated by Wachter et. al. and DeepFool methods for linear models. Finally, we empirically validate our theoretical findings using extensive experimentation with synthetic and real world datasets.

We study the problem of list-decodable linear regression, where an adversary can corrupt a majority of the examples. Specifically, we are given a set $T$ of labeled examples $(x, y) \in \mathbb{R}^d \times \mathbb{R}$ and a parameter $0< \alpha <1/2$ such that an $\alpha$-fraction of the points in $T$ are i.i.d. samples from a linear regression model with Gaussian covariates, and the remaining $(1-\alpha)$-fraction of the points are drawn from an arbitrary noise distribution. The goal is to output a small list of hypothesis vectors such that at least one of them is close to the target regression vector. Our main result is a Statistical Query (SQ) lower bound of $d^{\mathrm{poly}(1/\alpha)}$ for this problem. Our SQ lower bound qualitatively matches the performance of previously developed algorithms, providing evidence that current upper bounds for this task are nearly best possible.

Nowadays new technologies, and especially artificial intelligence, are more and more established in our society. Big data analysis and machine learning, two sub-fields of artificial intelligence, are at the core of many recent breakthroughs in many application fields (e.g., medicine, communication, finance, ...), including some that are strongly related to our day-to-day life (e.g., social networks, computers, smartphones, ...). In machine learning, significant improvements are usually achieved at the price of an increasing computational complexity and thanks to bigger datasets. Currently, cutting-edge models built by the most advanced machine learning algorithms typically became simultaneously very efficient and profitable but also extremely complex. Their complexity is to such an extent that these models are commonly seen as black-boxes providing a prediction or a decision which can not be interpreted or justified. Nevertheless, whether these models are used autonomously or as a simple decision-making support tool, they are already being used in machine learning applications where health and human life are at stake. Therefore, it appears to be an obvious necessity not to blindly believe everything coming out of those models without a detailed understanding of their predictions or decisions. Accordingly, this thesis aims at improving the interpretability of models built by a specific family of machine learning algorithms, the so-called tree-based methods. Several mechanisms have been proposed to interpret these models and we aim along this thesis to improve their understanding, study their properties, and define their limitations.