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  Minimum Divergence Methods in Statistical Machine Learning (eBook, PDF)

  This book explores minimum divergence methods of statistical machine learning for estimation, regression, prediction, and so forth, in which we engage in information geometry to elucidate their intrinsic properties of the corresponding loss functions, learning algorithms, and statistical models. One of the most elementary examples is Gauss's least squares estimator in a linear regression model, in which the estimator is given by minimization of the sum of squares between a response vector and a vector of the linear subspace hulled by explanatory vectors. This is extended to Fisher's maximum likelihood estimator (MLE) for an exponential model, in which the estimator is provided by minimization of the Kullback-Leibler (KL) divergence between a data distribution and a parametric distribution of the exponential model in an empirical analogue. Thus, we envisage a geometric interpretation of such minimization procedures such that a right triangle is kept with Pythagorean identity in the sense of the KL divergence. This understanding sublimates a dualistic interplay between a statistical estimation and model, which requires dual geodesic paths, called m-geodesic and e-geodesic paths, in a framework of information geometry. We extend such a dualistic structure of the MLE and exponential model to that of the minimum divergence estimator and the maximum entropy model, which is applied to robust statistics, maximum entropy, density estimation, principal component analysis, independent component analysis, regression analysis, manifold learning, boosting algorithm, clustering, dynamic treatment regimes, and so forth. We consider a variety of information divergence measures typically including KL divergence to express departure from one probability distribution to another. An information divergence is decomposed into the cross-entropy and the (diagonal) entropy in which the entropy associates with a generative model as a family of maximum entropy distributions; the cross entropy associates with a statistical estimation method via minimization of the empirical analogue based on given data. Thus any statistical divergence includes an intrinsic object between the generative model and the estimation method. Typically, KL divergence leads to the exponential model and the maximum likelihood estimation. It is shown that any information divergence leads to a Riemannian metric and a pair of the linear connections in the framework of information geometry. We focus on a class of information divergence generated by an increasing and convex function U, called U-divergence. It is shown that any generator function U generates the U-entropy and U-divergence, in which there is a dualistic structure between the U-divergence method and the maximum U-entropy model. We observe that a specific choice of U leads to a robust statistical procedure via the minimum U-divergence method. If U is selected as an exponential function, then the corresponding U-entropy and U-divergence are reduced to the Boltzmann-Shanon entropy and the KL divergence; the minimum U-divergence estimator is equivalent to the MLE. For robust supervised learning to predict a class label we observe that the U-boosting algorithm performs well for contamination of mislabel examples if U is appropriately selected. We present such maximal U-entropy and minimum U-divergence methods, in particular, selecting a power function as U to provide flexible performance in statistical machine learning.

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  Yeshua's Yoga: The Non-Dual Consciousness Teachings of the Gospel of Thomas , Hörbuch, Digital, ungekürzt, 470min

  The Gospel of Thomas, unearthed in Nag Hammadi Egypt in 1945, remains one of the most exciting archeological finds of recent centuries. But how prepared are we to approach this text on its own terms? How accurately are we able to discover what it is saying, immersed as we are in 2000 years of Platonic and dualistic Christian orthodoxy? Thanks to the influx of Eastern knowledge and the new crop of Western teachers willing to reapproach their Christian tradition as the Eastern event that Jesus was, we may finally be able to see the meaning and philosophical structure of this ancient and truly remarkable text. The Gospel of Thomas delineates the Way of Yeshua, a spiritual path that guides us through six clear movements of searching, finding, trouble, wonder, reigning, and rest. The resonance with classic Yogic paths makes this document the bridge many searchers need to reconcile and fully embrace the wisdom of both the East and the West. ungekürzt. Language: English. Narrator: Jack Nolan. Audio sample: https://samples.audible.de/bk/acx0/023268/bk_acx0_023268_sample.mp3. Digital audiobook in aax.

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  Persian Influence on Daniel and Jewish Apocalyptic Literature (eBook, PDF)

  Vicente Dobroruka explores Iranian influence on Second Temple Judaism, providing a new explanation of Persian culture and history in the context of biblical accounts by focusing on the spread of Zoroastrian ideas in the period c.300 BCE-200 CE.Dobroruka begins his investigation with an overview of the problems posed by a dualistic worldview-he examines the Indo-European origins of Zarathushtra and his ideas, explores the long-term implications for the notion of free-will, and clarifies the lightness/darkness paradigm that originated in Persia. Following this, Dobroruka discusses a variety of concepts that illustrate this influence, such as the role of matter and the material world, aspects of dualism and the cosmic struggle, the perspectives on the rewards for the just and the opposing punishments for the wicked, the idea of an 'Anointed One', shamanistic visionary experience, the resurrection, and the concepts of Sheol and Paradise.

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  • Price: 74.95 EUR excl. shipping
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  The Yoga of Ordinary Living , Hörbuch, Digital, ungekürzt, 420min

  Spiritual disciplines often seem remote from the realities of our daily lives. Yet there is a Mahayana Scripture which presents a model of enlightened practice in the midst of urban living, the Vimalakirti Sutra. This teaches a non-dualistic wisdom and reconciliation of dichotomies. It challenges ordinariness and reveals systematic and effective ways of tapping higher potentials while upholding one's usual responsibilities and enriching long-term relationships. Robert Thurman examines one of the most sacred texts of Mahayana Buddhism, The Vimalakirti-nirdesha Sutra. To any Buddhist practitioner, particularly those of Vajrayana Buddhism and Zen, this sutra is of the utmost importance. Unlike most sutras, its central figure is not a Buddha, but an ordinary man, who, in his mastery of the doctrine and religious practice, personifies the ideal lay believer, assuring commoners that they can reach levels of spiritual attainment comparable to those accessible to monks. The sutra teaches, among other subjects, the meaning of non-duality. Thurman discusses the background of the sutra, its place in the development of Buddhist thought, and the profundities of its principal doctrine: emptiness. ungekürzt. Language: English. Narrator: Robert Thurman. Audio sample: https://samples.audible.de/bk/brll/006462/bk_brll_006462_sample.mp3. Digital audiobook in aax.

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  The Island of Knowledge: The Limits of Science and the Search for Meaning , Hörbuch, Digital, ungekürzt, 633min

  Why discovering the limits to science may be the most powerful discovery of all. How much can we know about the world? In this audiobook physicist Marcelo Gleiser traces our search for answers to the most fundamental questions of existence, the origin of the universe, the nature of reality, and the limits of knowledge. In so doing he reaches a provocative conclusion: Science, like religion, is fundamentally limited as a tool for understanding the world. As science and its philosophical interpretations advance, we face the unsettling recognition of how much we don't know. Gleiser shows that by abandoning the dualistic model that divides reality into the known and the unknown, we can embark on a third way based on the acceptance of our limitations. Only then, he argues, will we be truly able to experience freedom, for to be free in an age of science we cannot turn science into a god. Gleiser ultimately offers an uplifting exploration of humanity's longing to conquer the unknown and of science's power to transform and inspire. PLEASE NOTE: When you purchase this title, the accompanying reference material will be available in your My Library section along with the audio. ungekürzt. Language: English. Narrator: William Neenan. Audio sample: https://samples.audible.de/bk/adbl/022313/bk_adbl_022313_sample.mp3. Digital audiobook in aax.

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  The Hidden Message of the Lost Gospel of Thomas: Exploring the Ancient Practice of Unitive Christianity , Hörbuch, Digital, ungekürzt, 455min

  Previously published as Yeshua's Yoga, The Hidden Message of the Lost Gospel of Thomas unearths the central teaching of this ancient text. The Gospel of Thomas, re-discovered in Nag Hammadi Egypt in 1945, remains one of the most exciting archaeological finds of recent centuries. But how prepared are we to approach this text on its own terms? How accurately are we able to discover what it is saying, immersed as we are in 2000 years of Platonic and dualistic Christian orthodoxy? Thanks to the influx of Eastern knowledge and the new crop of Western teachers willing to re-approach their Christian tradition as the Eastern wisdom teacher that Jesus was, we may finally be able to see the meaning and philosophical structure of this once-beloved and truly remarkable Christian text. The Gospel of Thomas delineates the Way of Yeshua, a spiritual path that guides us through six clear movements of searching, finding, trouble, wonder, reigning, and rest. The resonance with classic Yogic paths makes this document the bridge many searchers need to reconcile and fully embrace the wisdom of both the East and the West. ungekürzt. Language: English. Narrator: Jack Nolan. Audio sample: https://samples.audible.de/bk/acx0/040791/bk_acx0_040791_sample.mp3. Digital audiobook in aax.

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  The Bond Code: Dark Secrets of Ian Fleming and James Bond , Hörbuch, Digital, ungekürzt, 90min

  Ian Fleming was a true visionary, a dualistic individual who spent much time in his early life in a "special" school in Austria. It was here where he learned the sacred ways of the early Gnostics and Occultists and developed the very root of the enigmatic secret and eternal charisma of James Bond. Fleming explicitly said that Bond was Manichean, a distinctly Gnostic concept. The Bond books and films are strategically seeded with alchemical and Gnostic references for those with "the eyes to see". Fleming associated with mystics and initiated individuals around the globe. In the Bond Code, we shall see how deep this web of the occult truly went. Fleming lived in a fantasy world that led him into a land of sinister and esoteric thought. He created his own alter-ego as a great alchemical work to fulfill his own tumultuous and chaotic mind, and he left behind a set of clues and codes for us to decipher. Philip Gardiner finally unravels the secret of James Bond, piece by piece, radically reappraising everything we thought we knew about this secret agent and his creator. ungekürzt. Language: English. Narrator: Philip Gardiner. Audio sample: https://samples.audible.de/bk/real/000034/bk_real_000034_sample.mp3. Digital audiobook in aax.

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  Essence of Buddhism: An Introduction to Its Philosophy and Practice , Hörbuch, Digital, ungekürzt, 448min

  This lucid overview of the Buddhist path takes the perspective of the three "vehicles" of Tibetan Buddhism: the Hinayana, Mahayana, and Vajrayana. While these vehicles are usually presented as a historical development, they are here equated with the attitudes that individuals bring to their Buddhist practice. Basic to them all, however, is the need to understand our own immediate condition. The primary tool for achieving this is meditation, and The Essence of Buddhism serves as a handbook for the various meditative approaches of Buddhist practice. Beginning with the Four Noble Truths, Traleg Rinpoche incorporates the expansive vision of the bodhisattva path and the transformative vision of Tantra. The final chapters present the transcendent view of Mahamudra. This view dispenses with all dualistic fixations and directly realizes the natural freedom of the mind itself. Along the way, the author provides vivid definitions of fundamental concepts such as compassion, emptiness, and Buddha-nature, and answers common questions: Why does Buddhism teach that there is "no self"? Are Buddhist teachings pessimistic? Does Buddhism encourage social passivity? What is the role of sex in Buddhist Tantra? Why is it said that "samsara is nirvana"? Does it take countless lifetimes to attain enlightenment, or can it be achieved in a moment? ungekürzt. Language: English. Narrator: Paul Ansdell. Audio sample: https://samples.audible.de/bk/adbl/019874/bk_adbl_019874_sample.mp3. Digital audiobook in aax.

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  Muses: Revealing the Nature of Inspiration , Hörbuch, Digital, ungekürzt, 217min

  Muses have fascinated for millennia yet seldom receive as much exposure as the artistic geniuses they inspire. Of any age, descent or gender, muses enchant simply by being themselves; this innate capacity to inspire has been commonplace for many years yet these catalysing forces are little understood.New science places much emphasis on the role of the observer as the catalyst or creator of reality, and explains what is happening 'energetically' when two human beings relate to each other in the same space and time - or even when they're not in each others' presence.Challenging dualistic Cartesian philosophy and classical Newtonian physics by proposing an interconnected, quantum view of the world, new science can help us to better understand the magic of muses and it can even help us to channel inspiration more prominently into our everyday lives.Offering an 'ecology' of inspiration, Muses lends a fresh perspective to what happened when Lewis Carroll played with Alice Liddell; when Rainer Maria Rilke dreamt of Lou Andreas Salomé, or when John Lennon wrote for his one and only Yoko Ono. Taking this new insight to the edges of the 21st century, the book finishes with a chapter on the future of inspiration. ungekürzt. Language: English. Narrator: Peter Sandon. Audio sample: https://samples.audible.de/bk/summ/000194/bk_summ_000194_sample.mp3. Digital audiobook in aax.

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  The Shadow Effect: Illuminating the Hidden Power of Your True Self , Hörbuch, Digital, ungekürzt, 434min

  Deepak Chopra, Debbie Ford, and Marianne Williamson - New York Times best-selling authors and internationally acclaimed teachers - have joined together to share their knowledge on one of the most crucial obstacles to happiness we face: the shadow. These three luminaries, each with a signature approach, bring to light the parts of ourselves we deny but that still direct our life. For it is only when we embrace our shadow that we discover the gifts of our authentic nature. The shadow exists within all of us. It is a part of us and yet we spend most of our life running from it. But far from being scary, our dark side holds the promise of a better, more fulfilling life. Our shadow makes itself known every day. It is the reason we get furious over a friend showing up 10 minutes late, yell at our parents or kids when they have done nothing wrong, and sabotage our own success at the worst possible time. Until we are able to embrace our dualistic nature, we will continue to hurt ourselves and those closest to us and fall short of our potential. Combining the wisdom of three experts, The Shadow Effect is a practical and profound guide to discovering the gifts of our shadow. These three authors powerfully pierce the veil of our unclaimed self, releasing us from the past and propelling us on a journey to wholeness. No longer living a half life, we are capable of achieving our dreams and reclaiming the happiness that is our birthright. ungekürzt. Language: English. Narrator: Deepak Chopra, Marianne Williamson, Debbie Ford. Audio sample: https://samples.audible.de/bk/harp/002196/bk_harp_002196_sample.mp3. Digital audiobook in aax.

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  • Price: 9.95 EUR excl. shipping

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